Angles

Problem 101

Describe each type of angle: acute, right, obtuse, and straight. A. An obtuse angle measures less than 9090^{\circ} and an acute angle measures more than 9090^{\circ}, but less than 180180^{\circ}. A right angle measures 180180^{\circ} and a straight angle measures 9090^{\circ}. B. An acute angle measures less than 9090^{\circ} and an obtuse angle measures more than 9090^{\circ}, but less than 180180^{\circ}. A right angle measures 9090^{\circ} and a straight angle measures 180180^{\circ}. C. A right angle measures less than 9090^{\circ} and a straight angle measures more than 9090^{\circ}, but less than 180180^{\circ}. An acute angle measures 9090^{\circ} and an obtuse angle measures 180180^{\circ}. D. A straight angle measures less than 9090^{\circ} and a right angle measures more than 9090^{\circ}, but less than 180180^{\circ}. An obtuse angle measures 9090^{\circ} and an acute angle measures 180180^{\circ}.

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Problem 102

Find the measure of the complement and the supplement of 8585^{\circ}.
What is the measure of the complement of 8585^{\circ} ? \square What is the measure of the supplement of 8585^{\circ} ? \square

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Problem 103

What type of angle measures 3636^{\circ} ? adjacent obtuse acute opposite

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Problem 104

The total, TT, of the interior angles of a polygon with nn sides is given by T=180×(n2)T=180^{\circ} \times(n-2)
Calculate the total of the interior angles of this heptagon. Watch video

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Problem 105

I'm sorry, but I need more information to accurately rewrite the problem in LaTeX format. Could you provide additional details or context about the geometry problem involving the angle RUS\angle RUS?

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Problem 106

7 5 124° 6 3 4x 4 2 What is the value of x?

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Problem 107

What is the value of xx ?

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Problem 108

What is the value of xx ?

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Problem 109

Are all intersecting lines perpendicular? Draw a picture to help explain your answer. 3.GR.1.1

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Problem 110

Look at this diagram:
If HJundefined\overleftrightarrow{H J} and KMundefined\overleftrightarrow{K M} are parallel lines and mJIG=123m \angle J I G=123^{\circ}, what is mMLIm \angle M L I ? \square

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Problem 111

Given: ABBC\overline{A B} \cong \overline{B C} and BC\overline{B C} bisects ACD\angle A C D. Prove: ABCD\angle A \cong \angle B C D.
Note: quadrilateral properties are not permitted in this proof.
Step
1 try Type of Statement

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Problem 112

Here is Ethan's solution to the previous screen. Are these lines perpendicular? How do you know?
Use the sketch tool on the graph if that helps to illustrate your thinking.
I know that these lines are perpendicular because they are opposite recipricol of each other. Edit my response
Your classmates said: CAMRYN URIBE they have the opposite recipricol ALONDRA JUAREZ GUTIERREZ No they are not because they are opposite recipricol. ANTHONYMARTINEZ-VASQUEZ

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Problem 113

The slopes of perpendicular lines are

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Problem 114

The figure shows two parallel lines cut by a transversal.
Which angles are congruent to 7\angle 7 ?
Choose one option from each drop-down menu to answer the question. \angle \square Choose. and 7\angle 7 are congruent because they are
Choose... \square angles. \square Choose.. and 7\angle 7 are congruent because they are
Choose... \square angles. \square Choose.. and 7\angle 7 are congruent because they are Choose... \square angles. 8 9 10 11 12 10 of 14

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Problem 115

Solve for xx : x=x=\square

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Problem 116

Use the given information and theorems and postulates you have learned to show that cdc \| d.
18. m4=58,m6=58\mathrm{m} \angle 4=58^{\circ}, \mathrm{m} \angle 6=58^{\circ}
19. m1=(23x+38),m5=(17x+56),x=3\mathrm{m} \angle 1=(23 x+38)^{\circ}, \mathrm{m} \angle 5=(17 x+56)^{\circ}, x=3
20. m6=(12x+6),m3=(21x+9),x=5\mathrm{m} \angle 6=(12 x+6)^{\circ}, \mathrm{m} \angle 3=(21 x+9)^{\circ}, x=5
21. m1=99,m7=(13x+8),x=7\mathrm{m} \angle 1=99^{\circ}, \mathrm{m} \angle 7=(13 x+8)^{\circ}, x=7

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Problem 117

PRACTICE \& PROBLEM SOLVING APPLY
25. Model With Mathematics A glazier is setting supports in parallel segments to prevent glass breakage during storms. What are the values of xx and yy ? Justify your conclusions. () MP. 4
26. Reason In the parking lot shown, all of the lines for the parking spaces should be parallel. If m3=61m \angle 3=61, what should m1m \angle 1 and m2m \angle 2 be? Explain. (c) MP. 2
27. Communicate Precisely Margaret is in a boat traveling due west. She turned the boat 5050^{\circ} north of due west for a couple of minutes to get around a peninsula. Then she resumed due west again. (-) MP. 6 a. How many degrees would she turn the wheel to resume a due west course? b. What type of angle pair did she use? Are the angles congruent or supplementary?
8. Parallel lines mm and nn intersect parallel lines xx and yy, representing two sets of intersecting railroad tracks. If the minimum measure for 1\angle 1 is 101101^{\circ} and the maximum measure for 1\angle 1 is 106106^{\circ}, what are the minimum and maximum measures for 2\angle 2 ?

ASSESSMENT PRACTICE
29. Classify each angle as congruent to 1\angle 1 or congruent to 2\angle 2.
30. SAT/ACT In the diagram, aba \| b. What is m1m \angle 1 ? (A) 28 (C) 90 (B) 62 (D) 118
31. Performance Task Students on a scavenger hunt are given the map shown and several clues.

Part A The first clue states the following. Skyline Trail forms a transversal with Wood Path and Mission Path. Go to the corners that form same side exterior angles north of Skyline Trail. Which two corners does the clue mean? Use intersections and directions to explain. Part B If the second clue states the following, what trail marker should they go to? Wood and Mission Paths are parallel, and the northeast corner of Wood Path and Skyline Trail forms a 131131^{\circ} angle. The measure of the angle formed by the southwest corner of Skyline Trail and Mission Path is equal to the trail marker number on River Trail you must go to.

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Problem 118

7mOnundefined7 \widehat{m O n} et nOpundefined\widehat{n O p} sont deux angles adjacents supplementaires tels que mon =50n=50^{n}.
1. Calcule nop 22(O2^{2}(O,)estlabissecticedemon.(OW)cellede) est la bissectice de mon. (OW) celle de nop Calute xON0\mathrm{xON}_{0}

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Problem 119

3 The angles in each of these diagrams are all the same size. What is the size of each angle? a b

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Problem 120

The angles in each of these diagr the size of each angle? a

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Problem 121

Use the diagram and the given information to answer parts (a)-(d). - ADundefined\overleftrightarrow{A D} and EIundefined\overleftrightarrow{E I} are parallel. - JPundefined\overleftrightarrow{J P} and KOundefined\overleftrightarrow{K O} are transversals. - The measure of BCQ\angle B C Q is 6767^{\circ}. - The measure of QHI\angle Q H I is 119119^{\circ}. a. Find the measure of QFH\angle Q F H. b. What is the angle relationship between BCQ\angle B C Q and QFH\angle Q F H that verifies the measure of QFH\angle Q F H ? c. Find the measure of FQH\angle F Q H. d. What is the relationship between FQH,QFH\angle F Q H, \angle Q F H, and QHI\angle Q H I that verifies the measure of FQH\angle F Q H ? Copyri

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Problem 122

Use an algebraic equation to find the measure of each angle that is represented in terms of x 3x+20° 3x+40° ma 3x+20° ma 3x+40°

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Problem 123

16. Find the value of ee. e=e= \qquad
17. Find the value of vv. v=v= \qquad
18. Find xm//nx \| m / / n. x=x= \qquad
19. Find the missing angle २ = \qquad
21. Solve for xx. x=x= \qquad \qquad
22. Solve for xx. x=x=

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Problem 125

Which angles are vertical angles? IK\triangle I K and HIF\angle H I F JIK\angle J I K and JIF\angle J I F JIK\angle J I K and EFI\angle E F I IK\angle I K and EFD\angle E F D Submit

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Problem 126

16. In JKL\triangle J K L, if mKm \angle K is nine more than mJm \angle J and mLm \angle L is 21 less than twice mJm \angle J, find the meas of each angle. mJ=mK=mL=\begin{array}{l} m \angle J= \\ m \angle K= \\ m \angle L= \end{array}

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Problem 127

Hassan lined up the interior angles of the triangle along the line belou
What is the measure of the missing angle along the line?

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Problem 128

A. 1 B. 2 many angle measurements do you need to figure out the measurements of all the labeled angles the figure below? 1 2 4 3 C. 3 D. 4

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Problem 129

Question 2
Considérons le triangle RST représenté ci-dessous.
Quelle est, au degré près, la mesure de l'angle obtus RST? A) 9999^{\circ} B) 121121^{\circ} C) 127127^{\circ} D) 139139^{\circ}

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Problem 130

5. In parallelogram HIJK, the measure of angle H is 45 . a. Find the measure of angle JJ. Explain or show how you know. A diagram may be helpful. b. Find the measure of angle KK. Explain or show how you know.
6. The mQ=70m \angle Q=70^{\circ}. Find the mPm \angle P. You must explain or show how you arrived at your answer.

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Problem 131

In the figure, m1=(5x)m \angle 1=(5 x)^{\circ} and m2=(x6)m \angle 2=(x-6)^{\circ}. (b) Find the degree measure of each angle. m1=m2=\begin{array}{l} m \angle 1=\square^{\circ} \\ m \angle 2=\square^{\circ} \end{array} (a) Write an equation to find xx. Make sure you use an "=" sign in your answer.
Equation: \square
×\times 5

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Problem 132

7. Find the missing measures. \qquad \qquad a=b=c=d=\begin{array}{l} a=\overline{ } \\ b= \\ c= \\ d= \end{array} ?=?=

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Problem 133

In the figure, m1=(6x)m \angle 1=(6 x)^{\circ} and m2=(x+19)m \angle 2=(x+19)^{\circ}. (a) Write an equation to find XX, Make sure you use an " = " sign in your answer.
Equation: \square 1 2 (b) Find the degree measure of each angle. m1=m2=\begin{array}{l} m \angle 1=\square^{\circ} \\ m \angle 2=\square^{\circ} \end{array}

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Problem 136

4. m1m \wedge 1 \qquad Reason 5.

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Problem 137

A falcon dives toward the ground with a constant velocity of 5.10 m/s5.10 \mathrm{~m} / \mathrm{s} at 57.057.0^{\circ} below the horizontal. The Sun is directly overhead and casts a shadow of the falcon directly below it. What is the speed (in m/s\mathrm{m} / \mathrm{s} ) of its shadow on level ground? \square m/s\mathrm{m} / \mathrm{s} Need Help? Read It

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Problem 138

What is m1m \angle 1 ? m1=m \angle 1= \square Submit

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Problem 139

Determine the resultant of the vectors with the given magnitudes and directions. Positive angles are measured counterclockwise from the positive xx-axis, and negative angles are measured clockwise from the positive x-axis.
A: 568,150.0568,150.0^{\circ} B: 1248,226.01248,226.0^{\circ}
The magnitude of the resultant is 1491 . (Round to one decimal place as needed.) The direction of the resultant is \square^{\circ}. (Type your answer in degrees between 00^{\circ} and 360360^{\circ}. Round to one decimal place as needed.)

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Problem 140

Light Design. Determine the angle θ\theta in the design of the streetlight shown in the figure.
Angle θ\theta
The top angle
The bottom angle 20.7 127.2 32.1

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Problem 141

Calculate the size of angle xx.

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Problem 142

Use the following Lewis diagram for ethanol to answer the questions:
Remember that geometry refers to the geometry defined by the atoms, not the electron pairs. The geometry about atom 1 is \square .
The ideal value of the C-C-O angle at atom 2\mathbf{2} is \square degrees.
The geometry about atom 3 is \square . Submit Submit and Next \square : Mark this question for later review.

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Problem 143

The measure of JLM\angle J L M is 140140^{\circ}. The measure of JKL\angle J K L is 7575^{\circ}.
What is the measure of KJL\angle K J L ? Enter your answer in the box. mKJL=m \angle K J L=

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Problem 144

duding zero) depending on your answer. What is the measure of central angle AOBA O B to the nearest tenth a degree?
The measure of AOB\angle A O B is approximately \qquad degrees.
The solution is \square

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Problem 145

Which angles are alternate interior angles? YXU\angle Y X U and TUX\angle T U X YXU\angle Y X U and VUX\angle V U X YXU\angle Y X U and WXU\angle W X U YXU\angle Y X U and TUS\angle T U S

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Problem 146

Which angles are adjacent angles? ONQ\angle O N Q and RQN\angle R Q N ONQ\angle O N Q and MNL\angle M N L ONQ\angle O N Q and PQS\angle P Q S ONQ\angle O N Q and ONL\angle O N L

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Problem 147

Dalam Rajah 2, ABCDEFGH ialah sebuah oktagon sekata. Diberi bahawa HI dan GF ialah garis selari.
Cari nilai p p .
A 131 131^{\circ}
B 136 136^{\circ}
C 151 151^{\circ}
D 209 209^{\circ}

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Problem 148

55° 30° b C 30°

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Problem 149

Here is a 10-sided polygon 134° 168 Work out the value of x. 150 149 150 1299 125 168 Diagram NOT accurately drawn

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Problem 150

852736395057=85^{\circ} 27^{\prime} 36^{\prime \prime}-39^{\circ} 5057^{\prime \prime}=

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Problem 151

If CE\stackrel{C E}{ } and FHFH\stackrel{F H}{F H} are parallel lines and mCDB=110m \angle C D B=110^{\circ}, what is mFGDm \angle F G D ?

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Problem 152

If DFundefined\overleftrightarrow{D F} and GIundefined\overleftrightarrow{G I} are parallel lines and mDEH=47m \angle D E H=47^{\circ}, what is mIHJm \angle I H J ?

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Problem 153

In the opposite figure : If ABCD is a square and DEEB=25\frac{\mathrm{DE}}{\mathrm{EB}}=\frac{2}{5} , then tanθ=\tan \theta= (a) 73\frac{7}{3} (b) 37\frac{3}{7} (B) (c) 27\frac{2}{7} (d) 72\frac{7}{2}

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Problem 154

PROBLEM 20: The azimuth of the sides of a traverse ABCDEF are given below. Compute the internal angles. Bearing of AB=29045A B=290^{\circ} 45^{\circ} Bearing of BC=250+8B C=250^{\circ}+8^{\prime} Bearing of CD=19612C D=196^{\circ} 12^{\prime} Bearing of DE=17524D E=175^{\circ} 24^{\prime} Bearing of EF=11218E F=112^{\circ} 18^{\prime} Bearing of FA=3000F A=30^{\circ} 00^{\prime} Solution:

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Problem 155

3.3 In the diagram below, P,Q,R\mathrm{P}, \mathrm{Q}, \mathrm{R} and T are points on a circle with centre O . PR is a diameter of a circle. O^1=52\hat{\mathrm{O}}_{1}=52^{\circ}
Determine, with reasons the size of: 3.3.1 T^23.3 .1 \hat{\mathrm{~T}}_{2} 3.3.2 Q^2\hat{Q}_{2} 3.3.3 Q^1\hat{Q}_{1}

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Problem 156

In the figure below, m4=112m \angle 4=112^{\circ}. Find m<1,m2m<1, m \angle 2, and m<3m<3.

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Problem 157

In the figure below, m4=112m \angle 4=112^{\circ}. Find m1,m2m \angle 1, m \angle 2, and m3m \angle 3.

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Problem 158

In the figure below, m2=126m \angle 2=126^{\circ}. Find m1,m3m \angle 1, m \angle 3, and m4m \angle 4.

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Problem 159

Sketch θ=2π3\theta=-\frac{2 \pi}{3} in standard position.

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Problem 160

1. v=i+j,w=i+jv=i+j, w=-i+j A) Find the dot product vw\mathbf{v} \cdot \mathbf{w}. (1i+1j)(1i+1j)(1 i+1 j)(-1 i+1 j) B) Find the angle between v\mathbf{v} and w\mathbf{w}. C) State whether the vectors are parallel, orthogonal, or neither.

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Problem 161

The exterior angles of an octagon are marked on the diagram belov What is the sum of these angles?

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Problem 162

(From Unit 2, Lesson 3.)
4. Triangles ACDA C D and BCDB C D are isosceles. Angle BACB A C has a measure of 18 degrees and angle BDCB D C has a measure of 48 degrees.

The measure of angle ABDA B D is \qquad Show your work ADACand BDBCA D^{-} \cong A C^{-} \text {and } B D^{-} \cong B C^{-}

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Problem 163

Explore the properties of angles formed by two intersecting chords. 1.The intersecting chords form vertical angles. If mDEB=105m \angle D E B=105^{\circ}, then mAEC=m \angle A E C= \square mDEB=105m \angle \mathrm{DEB}=105^{\circ} Check

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Problem 164

In KLM,KLMK\triangle K L M, \overline{K L} \cong \overline{M K} and mK=141\mathrm{m} \angle K=141^{\circ}. Find mM\mathrm{m} \angle M.

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Problem 165

秘 The measure of an angle is 55^{\circ}. What is the measure of its supplementary angle?
Submit

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Problem 166

2{ }^{2} The measure of an angle is 4848^{\circ}. What is the measure of its supplementary angle? \square Submit

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Problem 167

he measure of an angle is 2929^{\circ}. What is the measure of its complementary angle?

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Problem 168

榋A, What is the value of pp ?

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Problem 169

Find xx. x=x=

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Problem 170

The measure of an angle is 21.921.9^{\circ}. What is the measure of its supplementary angle?

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Problem 171

The measure of an angle is 39.639.6^{\circ}. What is the measure of its complementary angle?

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Problem 172

斏, What is the value of zz ?

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Problem 173

Which angle is vertical to 2\angle 2 ? 4\angle 4 1\angle 1 3\angle 3 5\angle 5

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Problem 174

竛, Which angles are vertical to each other?

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Problem 175

In Exercises 17-20, write an equation of the line passing through point PP that is perpendicular to the given line. Graph the equations of the lines to check that they are perpendicular. (See Example 4.)
17. P(0,0),y=9x1P(0,0), y=-9 x-1
18. P(4,6),y=3P(4,-6), y=-3
19. P(2,3),y4=2(x+3)P(2,3), y-4=-2(x+3)
20. P(8,0),3x5y=6P(-8,0), 3 x-5 y=6

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Problem 176

Suppose that u\vec{u} and v\vec{v} are unit vectors in R3\mathbb{R}^{3}. If the angle between u\vec{u} and v\vec{v} is π/4\pi / 4, then what is the area of the parallelogram spanned by u\vec{u} and v\vec{v} ?
From the 7 options, select all that apply 12\frac{1}{\sqrt{2}} 2\sqrt{2} 2 12\frac{1}{2} 1 More info is needed to answer the question None of the above
3 attempts CHECK (2) HELP

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Problem 177

5. Let's find the value of xx in each of the following figures. a) e) b) f) c) g) d) h)

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Problem 178

Find (if possible) the complement and the supplement of each angle. (If not possible, enter IMPOSSIBLE.) (a) π10\frac{\pi}{10} complement \square radians supplement \square radians (b) 9π10\frac{9 \pi}{10} complement radians supplement \square radians

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Problem 179

Introduction to parallel lines cut by a transversal 1) List all of the acute angles in the diagram: \qquad 2) List all of the obtuse angles in the diagram: \qquad 3) List all of the vertical angles in the diagram: \qquad 4) List all of supplementary angles in the diagram. \qquad ***Challenge: If the measure of angle 2 in the diagram above is 4545^{\circ}, find the measure of all of the rest of the missing angles!***

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Problem 180

Two parallel lines are cut by a transversal as shown below. Suppose m8=52m \angle 8=52^{\circ}. Find m2m \angle 2 and m3m \angle 3. m2=m3=\begin{array}{l} m \angle 2=\square^{\circ} \\ m \angle 3=\square^{\circ} \end{array}

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Problem 181

In the figure shown to the right, one angle measurement is given. Find χp\chi_{p}. \qquad xp=x_{p}= \square 00^{\circ}

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Problem 182

(a) Sketch θ=330\theta=330^{\circ} in standard position.
Then sketch an angle between 360-360^{\circ} and 00^{\circ} that is coterminal with θ\theta.

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Problem 183

Answer the following. Round your answers to the nearest hundredth. (a) Convert 18π19-\frac{18 \pi}{19} radians to degree measure. \square (b) Convert -2.61 radians to degree measure. \square

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Problem 184

Below are two parallel lines with a third line intersecting them. x=x=\square^{\circ}

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Problem 185

right angle. Solve for xx.
Write an addition sentence using xx. x+x^{\circ}+ \square \square ={ }^{\circ}= - 1 2 3 4 5 6 7 8 9 0 Enter

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Problem 186

Find the measure of each missing angle. 8. m1=m2=m3=m4=\begin{array}{l} \mathrm{m} \angle 1= \\ \mathrm{m} \angle 2= \\ \mathrm{m} \angle 3= \\ \mathrm{m} \angle 4= \end{array}

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Problem 187

10. Choose the correct answer.
Given 1,2,4\angle 1, \angle 2, \angle 4, and 8\angle 8, which are vertical angles? 1\angle 1 and 2\angle 2 4\angle 4 and 8\angle 8 1\angle 1 and 4\angle 4 2\angle 2 and 4\angle 4

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Problem 188

d. 3\angle 3 and 6\angle 6 (9.) 5\angle 5 and 7\angle 7
2. Determine the sum of the measures of the interior angles of this polygon. [D]

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Problem 189

dent/3511142/25572425/87de596685885aeafa411311cfaaa61f
Triangle OPQO P Q is formed by connecting the midpoints of the side of triangle LMNL M N. The measures of the interior angles of triangle LMNL M N are shown. Find the measure of LOQ\angle L O Q. Figures not necessarily drawn to scale.

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Problem 190

NMLO VWXY\cong V W X Y. What is mXm \angle X ? \square Submit

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Problem 191

```latex \text{Given the expressions: } (7y-20), (5x-38), (3x-4), \text{ and the variable } m. \text{ If line } l \text{ is parallel to line } m, \text{ solve for } x \text{ and } y.

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Problem 192

9. In the diagram below, DE\overline{D E} is parallel to GK\overline{G K} and CA\overline{C A} is perpendicular to BA\overline{B A}. If mEAC=35m \angle E A C=35^{\circ} the of the following is the measure of ABC\angle A B C ? (1) 3535^{\circ} (2) 4545^{\circ} (3) 5555^{\circ} (4) 145145^{\circ}

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Problem 193

3. 4.
5. In Triangle MNO, N\angle N is 5 times the measure of M\angle M, and O\angle O is 4 times the measure of M\angle M. \qquad M=\angle M= \qquad J=\angle \mathrm{J}= \qquad G=H=I=\begin{array}{l} \angle G= \\ \angle H= \\ \angle I= \end{array} K=\angle K= \qquad L=\angle L= \qquad \qquad

4 \qquad N=\angle N= \qquad O=\angle O=

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Problem 194

19. Define the following terms: interior angle, exterior angle, remote interior angle, complementary angles, supplementary angles
20. Draw an example of each triangle and include the measure of each angle in your examples: acute triangle, equilateral triangle, right triangle, obtuse triangle.

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Problem 195

lyn Green Nov Determine whether lines m and n are parallel. Explain how you know.
1. n 2. m 89° 89°

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Problem 196

For problems 1 and 2 , use the diagram of lines ,m\ell, m, and tt. Assume m\ell \| m.
1. The measure of 1\angle 1 is 130130^{\circ}. a. What is the measure of 3\angle 3 ? b. Describe a sequence of rigid motions that verifies the measure of 3\angle 3.
2. The measure of 2\angle 2 is 5050^{\circ}. a. What is the measure of 6\angle 6 ? b. Describe a sequence of rigid motions that verifies the measure of 6\angle 6.

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Problem 197

Consider the diagram. a. Find the value of xx. b. Describe the angle relationship you used to find the value of xx.

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Problem 198

GIVEN: a e:12|\mid e: \angle 1 \cong \angle 2 PROVE: clld \begin{tabular}{|l|l|} \hline Stalemenis & Reasons \\ \hline & \\ \hline & \\ \hline & \\ \hline \end{tabular}

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Problem 199

111. В рівнобічній трапеції більша основа дорівнює 12 cm , а бічна сторона - 4 cm . Гострий кут трапеції дорівнює 60 . Знайти меншу основу трапеціі.

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Problem 200

В правильном тетраздре ABCDA B C D проведена высота DH.KD H . K - середина отрезка CH.BMC H . B M - медиана боковой грани BCDB C D. a) Докажите, что угол между DHD H и BMB M равен углу BMKB M K. б) Найдите угол между DH и BMB M.

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