Question

in the figure below, ao ⊥ cd, m∠aob = 63°. find the indicated angle measures. m∠aoc = select m∠bod = select m∠eof = select

Explanation:

Step1: Recall perpendicular - angle property

Since $AO\perp CD$, $\angle AOC = 90^{\circ}$.

Step2: Use vertical - angle property

$\angle AOB$ and $\angle BOD$ are vertical angles. Vertical angles are equal. So $m\angle BOD=m\angle AOB = 63^{\circ}$.

Step3: Use linear - pair and vertical - angle properties

$\angle AOB+\angle AOF = 180^{\circ}$ (linear - pair). So $\angle AOF=180^{\circ}-\angle AOB=180 - 63=117^{\circ}$. $\angle EOF$ and $\angle AOF$ are vertical angles, so $m\angle EOF=m\angle AOF = 117^{\circ}$.

Answer:

$m\angle AOC = 90^{\circ}$
$m\angle BOD = 63^{\circ}$
$m\angle EOF = 117^{\circ}$