Question

example 2 find unknown angle measures in the figure, ( a parallel b ). what are the measures of ( angle 4 ) and ( angle 5 )? explain. use what you know about the angles created when parallel lines are cut by a transversal. ( mangle 4 = 99^circ ) the ( 99^circ ) angle and ( angle 4 ) are corresponding angles. ( mangle 4 + mangle 5 = 180^circ ) ( angle 4 ) and ( angle 5 ) are supplementary angles. ( mangle 5 = 180^circ - 99^circ ) ( mangle 5 = 81^circ ) try it! what are the measures of ( angle 7 ) and ( angle 2 )? explain.

Explanation:

Step1: Relate ∠1 to ∠4

$\angle 1$ and $\angle 4$ are vertical angles, so $m\angle 1 = m\angle 4 = 99^\circ$

Step2: Relate ∠2 to ∠5

$\angle 2$ and $\angle 5$ are vertical angles, so $m\angle 2 = m\angle 5 = 81^\circ$

Answer:

The measure of $\angle 1$ is $99^\circ$, and the measure of $\angle 2$ is $81^\circ$. $\angle 1$ is congruent to $\angle 4$ (vertical angles), and $\angle 2$ is congruent to $\angle 5$ (vertical angles).