Question

if ∠3 measures 105°, then what is the measure of

a. 75°
b. 85°
c. 105°
d. 180°

Explanation:

Step1: Identify angle - pair relationship

$\angle3$ and $\angle1$ are vertical angles, and $\angle3$ and $\angle2$ are supplementary angles.

Step2: Use supplementary - angle property

Supplementary angles add up to $180^{\circ}$. Let the measure of $\angle2$ be $x$. Then $x + 105^{\circ}=180^{\circ}$.

Step3: Solve for the angle measure

$x=180^{\circ}- 105^{\circ}=75^{\circ}$

Answer:

A. $75^{\circ}$