Question

1. find the measure of each angle.

a. ∠1 and ∠2 form a linear pair and m∠2 = 52°. find m∠1.
b. ∠3 and ∠4 are vertical angles and m∠3 = 132°. find m∠4.

Explanation:

Step1: Recall linear - pair property

The sum of angles in a linear pair is 180°. So, $m\angle1 + m\angle2=180^{\circ}$.

Step2: Solve for $m\angle1$

Given $m\angle2 = 52^{\circ}$, then $m\angle1=180^{\circ}-m\angle2$. Substitute $m\angle2 = 52^{\circ}$ into the equation: $m\angle1 = 180 - 52=128^{\circ}$.

Step3: Recall vertical - angles property

Vertical angles are congruent. So, if $\angle3$ and $\angle4$ are vertical angles, then $m\angle3=m\angle4$.

Step4: Find $m\angle4$

Given $m\angle3 = 132^{\circ}$, then $m\angle4 = 132^{\circ}$.

Answer:

a. $m\angle1 = 128^{\circ}$
b. $m\angle4 = 132^{\circ}$