Question

if the measure of angle 2 is equal to 45 degrees what is the measure of angle 3? 135 0

Explanation:

Step1: Identify angle - relationship

Angle 2 and angle 3 are vertical angles. Vertical angles are equal.

Step2: Determine angle 3 measure

Since $\angle2 = 45^{\circ}$ and $\angle2=\angle3$ (vertical - angle property), then $\angle3 = 45^{\circ}$. But this is not in the options. If we assume angle 2 and angle 3 are supplementary (a common mis - interpretation if they are adjacent - like angles formed by two lines), and supplementary angles add up to $180^{\circ}$.
Let $\angle2 = 45^{\circ}$, and $\angle2+\angle3=180^{\circ}$.
We solve for $\angle3$: $\angle3=180^{\circ}-\angle2$.
Substitute $\angle2 = 45^{\circ}$ into the formula: $\angle3 = 180 - 45=135^{\circ}$.

Answer:

$135$