Question

Parallel Lines Relay Race answer key D please help​

Answer 1

1) 10

2) 16

3) 3

4) 23

Explanation:

Problems related to Parallel lines:

1. If two parallel lines are intersected by a transversal, then the alternate exterior angles are equal.

9x - 29 = 5x + 11

Add 29 to both sides,

9x = 5x + 11 + 29

9x = 5x + 40

Subtract '5x' from both sides,

9x - 5x = 40

4x = 40

Divide both sides by 4,

x = 40 ÷ 4

`\boxed{\bf x = 10}`

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2) If two parallel lines are intersected by a transversal, then the alternate interior angles are equal.

`\sf 10x - 42 = 8x - \boxed{10}`

Add 42 to both sides,

10x = 8x - 10 + 42

10x = 8x + 32

Subtract '8x' from both sides,

10x - 8x = 32

2x = 32

Divide both sides by 2,

x = 32÷ 2

`\boxed{\bf x = 16}`

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3) If two parallel lines are intersected by a transversal, then the Co-interior angles are supplementary.

`\sf 36x + \boxed{16} +17x + 5 = 180`

36x + 17x + 16 + 5 = 180

Combine like terms,

53x + 21 = 180

Subtract 21 form both sides,

53x = 180 - 21

53x = 159

Divide both sides by 53,

x = 159 ÷ 53

`\boxed{\bf x = 3}`

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4) If two parallel lines are intersected by a transversal, then the corresponding angles are equal.

`\boxed{3}x + 7 = 99 - x`

Add x to both sides,

3x + x + 7 = 99

4x + 7 = 99

Subtract 7 from both sides,

4x = 99 -7

4x = 92

Divide both sides by 4,

x = 92 ÷ 4

`\boxed{\bf x = 23}`

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Answer:

1) x = 10

2) x = 16

3) x = 3

4) x = 23