Answer:
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

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

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

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

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

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

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

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Answer:
1) x = 10
2) x = 16
3) x = 3
4) x = 23