Question

if $ef = eh = 22$, $m\angle egf = 9p$, and $m\angle egh = p + 56^\circ$, what is the value of $p$?
$p = \square^\circ$

Explanation:

Step1: Identify angle bisector property

Since $EF = EH$, and $EF \perp GF$, $EH \perp GH$, $GE$ bisects $\angle HGF$. So $\angle EGH = \angle EGF$.

Step2: Set up equation for angles

Substitute the given angle expressions:
$p + 56 = 9p$

Step3: Solve for $p$

Rearrange to isolate $p$:
$56 = 9p - p$
$56 = 8p$
$p = \frac{56}{8}$

Answer:

$7$