Math / Geometry

QuestionName: $\qquad$ $11-18-2024$
Chapter 1 \& 3 Review
1. Vertical angles are Qpposite angles. that are congruent.
2. Same - side interior angles are Between the 2 lines on the same side,
3. Alternate interior angles are Between the 2 lines on opposite sides Given the diagram at the right... name the special type of angle.
4. $<3 \&<6$ are $\qquad$ Alt - Int angles.
5. $<1 \&<8$ are Alt-Ext $\qquad$ angles.
6. Using the same diagram, if $m<4=85^{\circ}$ , find $m<8$ . $m \angle 8=85^{\circ}$ because theyre corresponding (congruent)
7. Given the diagram, name the angle in 3 ways. $\begin{array}{l} \angle B S T \\ \angle T S \beta \end{array}$
8. $\angle A \& \angle B$ are supplementary. If $\angle A=98^{\circ}$ , find $m<B$ . $\begin{array}{c} 180-98=82^{\circ} \\ m \angle 82^{\circ} \end{array}$
9. $\angle C \&<D$ are complementary. If $<D=22^{\circ}$ , find $\angle C$ . $c \angle 2 \partial^{\circ}$ becaus theyre corresponding congruens) The same.

Studdy Solution

STEP 1

1. Vertical angles are congruent.
2. Same-side interior angles are supplementary when lines are parallel.
3. Alternate interior angles are congruent when lines are parallel.
4. Corresponding angles are congruent when lines are parallel.
5. Supplementary angles sum to $180^\circ$ .
6. Complementary angles sum to $90^\circ$ .

STEP 2

1. Identify angle relationships.
2. Solve for unknown angles using given relationships and properties.

STEP 3

Identify the relationship between angles $<3$ and $<6$ . According to the problem, they are alternate interior angles. This means they are congruent if the lines are parallel.

STEP 4

Identify the relationship between angles $<1$ and $<8$ . According to the problem, they are alternate exterior angles. This means they are congruent if the lines are parallel.

STEP 5

Given that $m<4 = 85^\circ$ , find $m<8$ . Since $<4$ and $<8$ are corresponding angles, they are congruent. Therefore:
$m<8 = 85^\circ$

STEP 6

Name the angle in three ways. Given the angle $\angle BST$ , it can also be named as $\angle TSB$ and $\angle S$ .

STEP 7

Given $\angle A$ and $\angle B$ are supplementary and $\angle A = 98^\circ$ , find $m<B$ . Supplementary angles sum to $180^\circ$ , so:
$m<B = 180^\circ - 98^\circ = 82^\circ$

STEP 8

Given $\angle C$ and $<D$ are complementary and $<D = 22^\circ$ , find $\angle C$ . Complementary angles sum to $90^\circ$ , so:
$m<C = 90^\circ - 22^\circ = 68^\circ$
The solutions for the given problems are:
1. $<3$ and $<6$ are alternate interior angles.
2. $<1$ and $<8$ are alternate exterior angles.
3. $m<8 = 85^\circ$
4. Angle $\angle BST$ can be named as $\angle TSB$ and $\angle S$ .
5. $m<B = 82^\circ$
6. $m<C = 68^\circ$

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Studdy Solution

STEP 1

STEP 2

1. Identify angle relationships.
2. Solve for unknown angles using given relationships and properties.

STEP 3

Identify the relationship between angles $<3$ and $<6$ . According to the problem, they are alternate interior angles. This means they are congruent if the lines are parallel.

STEP 4

Identify the relationship between angles $<1$ and $<8$ . According to the problem, they are alternate exterior angles. This means they are congruent if the lines are parallel.

STEP 5

Given that $m<4 = 85^\circ$ , find $m<8$ . Since $<4$ and $<8$ are corresponding angles, they are congruent. Therefore:
$m<8 = 85^\circ$

STEP 6

Name the angle in three ways. Given the angle $\angle BST$ , it can also be named as $\angle TSB$ and $\angle S$ .

STEP 7

Given $\angle A$ and $\angle B$ are supplementary and $\angle A = 98^\circ$ , find $m<B$ . Supplementary angles sum to $180^\circ$ , so:
$m<B = 180^\circ - 98^\circ = 82^\circ$

STEP 8

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Studdy Solution

STEP 1

STEP 2

1. Identify angle relationships.2. Solve for unknown angles using given relationships and properties.

STEP 3

Identify the relationship between angles <3<3<3 and <6<6<6. According to the problem, they are alternate interior angles. This means they are congruent if the lines are parallel.

STEP 4

Identify the relationship between angles <1<1<1 and <8<8<8. According to the problem, they are alternate exterior angles. This means they are congruent if the lines are parallel.

STEP 5

Given that m<4=85∘m<4 = 85^\circm<4=85∘, find m<8m<8m<8. Since <4<4<4 and <8<8<8 are corresponding angles, they are congruent. Therefore:m<8=85∘ m<8 = 85^\circ m<8=85∘

STEP 6

Name the angle in three ways. Given the angle ∠BST\angle BST∠BST, it can also be named as ∠TSB\angle TSB∠TSB and ∠S\angle S∠S.

STEP 7

Given ∠A\angle A∠A and ∠B\angle B∠B are supplementary and ∠A=98∘\angle A = 98^\circ∠A=98∘, find m<Bm<Bm<B. Supplementary angles sum to 180∘180^\circ180∘, so:m<B=180∘−98∘=82∘ m<B = 180^\circ - 98^\circ = 82^\circ m<B=180∘−98∘=82∘

STEP 8

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1. Identify angle relationships.
2. Solve for unknown angles using given relationships and properties.

Identify the relationship between angles $<3$ and $<6$ . According to the problem, they are alternate interior angles. This means they are congruent if the lines are parallel.

Identify the relationship between angles $<1$ and $<8$ . According to the problem, they are alternate exterior angles. This means they are congruent if the lines are parallel.

Given that $m<4 = 85^\circ$ , find $m<8$ . Since $<4$ and $<8$ are corresponding angles, they are congruent. Therefore:
$m<8 = 85^\circ$

Name the angle in three ways. Given the angle $\angle BST$ , it can also be named as $\angle TSB$ and $\angle S$ .

Given $\angle A$ and $\angle B$ are supplementary and $\angle A = 98^\circ$ , find $m<B$ . Supplementary angles sum to $180^\circ$ , so:
$m<B = 180^\circ - 98^\circ = 82^\circ$