Question

1. examine the given figure. if a = 30°, what is the average of angles c and d?

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, $a = c = 30^{\circ}$.

Step2: Use linear - pair property

$a$ and $d$ form a linear - pair, so $a + d=180^{\circ}$. Then $d = 180^{\circ}-a=180 - 30=150^{\circ}$.

Step3: Calculate the average

The average of $c$ and $d$ is $\frac{c + d}{2}=\frac{30^{\circ}+150^{\circ}}{2}=\frac{180^{\circ}}{2}=90^{\circ}$.

Answer:

$90^{\circ}$