Question

if ∠fhg ≅ ∠fhi, fg = p + 63, and fi = 4p, what is the value of p?

Explanation:

Step1: Apply angle - bisector theorem

Since $\angle FHG\cong\angle FHI$ and $HG\perp FG$, $HI\perp FI$, by the angle - bisector theorem, we know that $FG = FI$.
$p + 63=4p$

Step2: Solve the equation for $p$

Subtract $p$ from both sides of the equation:
$63 = 4p-p$
$63=3p$
Then divide both sides by 3:
$p=\frac{63}{3}$

Answer:

$21$