Question

if $ef = eh = 38$, $m\angle egf = t + 27^\circ$, and $m\angle egh = 2t$, what is the value of $t$?
(image of a geometric figure with right angles at $h$ and $f$, vertices $e$, $g$, $h$, $f$ as shown)
$t = \square^\circ$

Explanation:

Step1: Use the Angle - Bisector Theorem (Converse)

Since \(EF = EH = 38\) and \(EH\perp GH\), \(EF\perp GF\), then \(EG\) is the angle - bisector of \(\angle HGF\). So, \(m\angle EGF=m\angle EGH\).

Step2: Set up the equation

We know that \(m\angle EGF=t + 27^{\circ}\) and \(m\angle EGH = 2t\). Then the equation is \(t + 27=2t\).

Step3: Solve the equation for \(t\)

Subtract \(t\) from both sides of the equation \(t + 27=2t\).
\(2t-t=27\).

Answer:

\(27\)