Question

1. let m∠1 = 120°. a. what is m∠5? how do you know? b. what is m∠6? how do you know? c. what is m∠8? how do you know?

Explanation:

Step1: Assume parallel lines and transversal

Assume there are parallel lines cut by a transversal. $\angle1$ and $\angle5$ are corresponding angles.

Step2: Use corresponding - angle property

Corresponding angles are congruent when lines are parallel. So $m\angle5 = m\angle1$.
$m\angle5=120^{\circ}$

Step3: Use linear - pair property for $\angle6$

$\angle1$ and $\angle6$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle6 = 180 - m\angle1$.
$m\angle6=180 - 120=60^{\circ}$

Step4: Use vertical - angle property for $\angle8$

$\angle1$ and $\angle8$ are vertical angles. Vertical angles are congruent. So $m\angle8 = m\angle1$.
$m\angle8 = 120^{\circ}$

Answer:

a. $m\angle5 = 120^{\circ}$, because $\angle1$ and $\angle5$ are corresponding angles.
b. $m\angle6 = 60^{\circ}$, because $\angle1$ and $\angle6$ form a linear pair.
c. $m\angle8 = 120^{\circ}$, because $\angle1$ and $\angle8$ are vertical angles.