Question

1. find $m\angle 1$ and $m\angle 2$.
2. find the values of $x$ and $y$.

Explanation:

Problem 8

Step1: Identify vertical angle

$m\angle 1 = 119^\circ$ (vertical angles are equal)

Step2: Identify supplementary angle

$m\angle 2 = 180^\circ - 119^\circ = 61^\circ$
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Problem 9

Step1: Identify vertical angle

$m\angle 1 = 71^\circ$ (vertical angles are equal)

Step2: Identify supplementary angle

$m\angle 2 = 180^\circ - 71^\circ = 109^\circ$
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Problem 10

Step1: Identify supplementary angle

$x = 180^\circ - 70^\circ = 110^\circ$
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Problem 11

Step1: Identify vertical angle

$x = 81^\circ$ (vertical angles are equal)

Step2: Identify supplementary angle

$y = 180^\circ - 81^\circ = 99^\circ$
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Problem 12

Step1: Identify vertical angle

$x = 89^\circ$ (vertical angles are equal)

Step2: Identify supplementary angle

$y = 180^\circ - 89^\circ = 91^\circ$
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Problem 13

Step1: Identify right angle

$x = 90^\circ$ (perpendicular lines form right angles)

Answer:

Problem 8: $m\angle 1 = 119^\circ$, $m\angle 2 = 61^\circ$
Problem 9: $m\angle 1 = 71^\circ$, $m\angle 2 = 109^\circ$
Problem 10: $x = 110^\circ$
Problem 11: $x = 81^\circ$, $y = 99^\circ$
Problem 12: $x = 89^\circ$, $y = 91^\circ$
Problem 13: $x = 90^\circ$