Math / Geometry

Question16. Find the value of $e$ . $e=$ $\qquad$
17. Find the value of $v$ . $v=$ $\qquad$
18. Find $x \| m / / n$ . $x=$ $\qquad$
19. Find the missing angle २ = $\qquad$
21. Solve for $x$ . $x=$ $\qquad$ $\qquad$
22. Solve for $x$ . $x=$

Studdy Solution

STEP 1

What is this asking? We've got a bunch of geometry puzzles to crack, finding missing angles and variables in lines, triangles, and parallel lines! Watch out! Remember those angle relationships – supplementary, complementary, vertical angles, corresponding angles, and the angles in a triangle adding up to $180^\circ$ !

STEP 2

1. Solve for e.
2. Solve for v.
3. Solve for x with parallel lines.
4. Find the missing angle in the triangle.
5. Solve for x in the right triangle.
6. Solve for x in the triangle.

STEP 3

The angles $110^\circ$ and $(9e - 7)^\circ$ are on a straight line, so they're supplementary angles.
This means they add up to $180^\circ$ !

STEP 4

Let's set up our equation: $110 + (9e - 7) = 180$ .

STEP 5

Simplify and solve: $9e + 103 = 180$ .
Subtract 103 from both sides to get $9e = 77$ .

STEP 6

Divide both sides by 9 to find $e = \frac{77}{9}$ .

STEP 7

The angles $50^\circ$ and $(v - 7)^\circ$ are vertical angles, meaning they're equal!

STEP 8

Set up the equation: $v - 7 = 50$ .

STEP 9

Add 7 to both sides to find $v = 57$ .

STEP 10

Since the lines m and n are parallel, the given angles are corresponding angles, and corresponding angles are equal!

STEP 11

Set up the equation: $3x + 7 = 60$ .

STEP 12

Subtract 7 from both sides: $3x = 53$ .

STEP 13

Divide both sides by 3: $x = \frac{53}{3}$ .

STEP 14

The angles in a triangle add up to $180^\circ$ .
We have two angles, $50^\circ$ and $85^\circ$ , and we need to find the third.

STEP 15

Let the missing angle be $\alpha$ .
The equation is $50 + 85 + \alpha = 180$ .

STEP 16

Simplify: $135 + \alpha = 180$ .

STEP 17

Subtract 135 from both sides: $\alpha = 45^\circ$ .

STEP 18

This problem is missing from the image, but we'll leave the section here in case it's needed later.

STEP 19

The angles in a triangle add up to $180^\circ$ .
Our angles are $7x + 6$ , $4x + 8$ , and $102^\circ$ .

STEP 20

Set up the equation: $(7x + 6) + (4x + 8) + 102 = 180$ .

STEP 21

Combine like terms: $11x + 116 = 180$ .

STEP 22

Subtract 116 from both sides: $11x = 64$ .

STEP 23

Divide both sides by 11: $x = \frac{64}{11}$ .

STEP 24

$e = \frac{77}{9}$ $v = 57$ $x = \frac{53}{3}$ Missing angle = $45^\circ$ $x = \frac{64}{11}$

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Question16. Find the value of eee. e=e=e= \qquad17. Find the value of vvv. v=v=v= \qquad18. Find x∥m//nx \| m / / nx∥m//n. x=x=x= \qquad19. Find the missing angle २ = \qquad21. Solve for xxx. x=x=x= \qquad \qquad22. Solve for xxx. x=x=x=

Studdy Solution

STEP 1

STEP 2

1. Solve for *e*.2. Solve for *v*.3. Solve for *x* with parallel lines.4. Find the missing angle in the triangle.5. Solve for *x* in the right triangle.6. Solve for *x* in the triangle.

STEP 3

The angles 110∘110^\circ110∘ and (9e−7)∘(9e - 7)^\circ(9e−7)∘ are on a straight line, so they're **supplementary angles**.This means they add up to 180∘180^\circ180∘!

STEP 4

Let's set up our equation: 110+(9e−7)=180110 + (9e - 7) = 180110+(9e−7)=180.

STEP 5

Simplify and solve: 9e+103=1809e + 103 = 1809e+103=180.Subtract 103 from both sides to get 9e=779e = 779e=77.

STEP 6

Divide both sides by 9 to find e=779e = \frac{77}{9}e=977​.

STEP 7

The angles 50∘50^\circ50∘ and (v−7)∘(v - 7)^\circ(v−7)∘ are **vertical angles**, meaning they're equal!

STEP 8

Set up the equation: v−7=50v - 7 = 50v−7=50.

STEP 9

Add 7 to both sides to find v=57v = 57v=57.

STEP 10

Since the lines *m* and *n* are parallel, the given angles are **corresponding angles**, and corresponding angles are equal!

STEP 11

Set up the equation: 3x+7=603x + 7 = 603x+7=60.

STEP 12

Subtract 7 from both sides: 3x=533x = 533x=53.

STEP 13

Divide both sides by 3: x=533x = \frac{53}{3}x=353​.

STEP 14

The angles in a triangle add up to 180∘180^\circ180∘.We have two angles, 50∘50^\circ50∘ and 85∘85^\circ85∘, and we need to find the third.

STEP 15

Let the missing angle be α\alphaα.The equation is 50+85+α=18050 + 85 + \alpha = 18050+85+α=180.

STEP 16

Simplify: 135+α=180135 + \alpha = 180135+α=180.

STEP 17

Subtract 135 from both sides: α=45∘\alpha = 45^\circα=45∘.

STEP 18

This problem is missing from the image, but we'll leave the section here in case it's needed later.

STEP 19

The angles in a triangle add up to 180∘180^\circ180∘.Our angles are 7x+67x + 67x+6, 4x+84x + 84x+8, and 102∘102^\circ102∘.

STEP 20

Set up the equation: (7x+6)+(4x+8)+102=180(7x + 6) + (4x + 8) + 102 = 180(7x+6)+(4x+8)+102=180.

STEP 21

Combine like terms: 11x+116=18011x + 116 = 18011x+116=180.

STEP 22

Subtract 116 from both sides: 11x=6411x = 6411x=64.

STEP 23

Divide both sides by 11: x=6411x = \frac{64}{11}x=1164​.

STEP 24

e=779e = \frac{77}{9}e=977​ v=57v = 57v=57 x=533x = \frac{53}{3}x=353​Missing angle = 45∘45^\circ45∘ x=6411x = \frac{64}{11}x=1164​

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Question16. Find the value of $e$ . $e=$ $\qquad$
17. Find the value of $v$ . $v=$ $\qquad$
18. Find $x \| m / / n$ . $x=$ $\qquad$
19. Find the missing angle २ = $\qquad$
21. Solve for $x$ . $x=$ $\qquad$ $\qquad$
22. Solve for $x$ . $x=$

1. Solve for e.
2. Solve for v.
3. Solve for x with parallel lines.
4. Find the missing angle in the triangle.
5. Solve for x in the right triangle.
6. Solve for x in the triangle.

The angles $110^\circ$ and $(9e - 7)^\circ$ are on a straight line, so they're supplementary angles.
This means they add up to $180^\circ$ !

Let's set up our equation: $110 + (9e - 7) = 180$ .

Simplify and solve: $9e + 103 = 180$ .
Subtract 103 from both sides to get $9e = 77$ .

Divide both sides by 9 to find $e = \frac{77}{9}$ .

The angles $50^\circ$ and $(v - 7)^\circ$ are vertical angles, meaning they're equal!

Set up the equation: $v - 7 = 50$ .

Add 7 to both sides to find $v = 57$ .

Since the lines m and n are parallel, the given angles are corresponding angles, and corresponding angles are equal!

Set up the equation: $3x + 7 = 60$ .

Subtract 7 from both sides: $3x = 53$ .

Divide both sides by 3: $x = \frac{53}{3}$ .

The angles in a triangle add up to $180^\circ$ .
We have two angles, $50^\circ$ and $85^\circ$ , and we need to find the third.

Let the missing angle be $\alpha$ .
The equation is $50 + 85 + \alpha = 180$ .

Simplify: $135 + \alpha = 180$ .

Subtract 135 from both sides: $\alpha = 45^\circ$ .

The angles in a triangle add up to $180^\circ$ .
Our angles are $7x + 6$ , $4x + 8$ , and $102^\circ$ .

Set up the equation: $(7x + 6) + (4x + 8) + 102 = 180$ .

Combine like terms: $11x + 116 = 180$ .

Subtract 116 from both sides: $11x = 64$ .

Divide both sides by 11: $x = \frac{64}{11}$ .

$e = \frac{77}{9}$ $v = 57$ $x = \frac{53}{3}$ Missing angle = $45^\circ$ $x = \frac{64}{11}$