Question

if m∠fhg = m∠fhi = 63°, fg = t + 21, and fi = 2t, what is the value of t?

Explanation:

Step1: Apply angle - bisector theorem

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

Step2: Set up the equation

We are given that $FG=t + 21$ and $FI = 2t$. So, we set up the equation $t + 21=2t$.

Step3: Solve the equation

Subtract $t$ from both sides of the equation: $2t-t=21$.

Answer:

$21$