Question

1. examine the given figure. if angle r measures 45°, what is the measure of the sum of angles u and w?

Explanation:

Step1: Identify vertical - angle relationship

Angle $r$ and angle $v$ are vertical angles, so $\angle v=\angle r = 45^{\circ}$.

Step2: Use linear - pair property

Angles $u$ and $v$ form a linear pair, so $\angle u+\angle v = 180^{\circ}$, then $\angle u=180^{\circ}-\angle v=180 - 45=135^{\circ}$.

Step3: Identify right - angle

We know that one of the angles in the figure is a right - angle, and $\angle w = 90^{\circ}$.

Step4: Calculate the sum of $u$ and $w$

$\angle u+\angle w=135^{\circ}+90^{\circ}=225^{\circ}$.

Answer:

$225^{\circ}$