Question

ge is the angle bisector of ∠hgf. find m∠egf if m∠hge=(3x)° and m∠hgf = 36°.

Explanation:

Step1: Recall angle - bisector property

An angle bisector divides an angle into two equal angles. So, $m\angle HGE=m\angle EGF$.

Step2: Set up the equation

Since $m\angle HGE = m\angle EGF$ and $m\angle HGF=m\angle HGE + m\angle EGF = 36^{\circ}$, and $m\angle HGE=(3x)^{\circ}$, we have $3x+3x = 36$.
Combining like - terms gives $6x=36$.

Step3: Solve for $x$

Dividing both sides of the equation $6x = 36$ by 6, we get $x=\frac{36}{6}=6$.

Step4: Find $m\angle EGF$

Since $m\angle EGF=(3x)^{\circ}$ and $x = 6$, then $m\angle EGF=3\times6=18^{\circ}$.

Answer:

$x = 6$
$m\angle EGF=18^{\circ}$