Question

find m∠hji.

Explanation:

Step1: Identify triangle type

The triangle has two sides marked congruent, so it is isosceles with $\overline{JI} \cong \overline{HI}$. This means the base angles opposite these sides are congruent: $\angle HJI \cong \angle JHI$.

Step2: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$. Let $m\angle HJI = x$. Then $m\angle JHI = x$, and $m\angle H = 64^\circ$.

Step3: Set up and solve equation

$$x + x + 64^\circ = 180^\circ$$
$$2x = 180^\circ - 64^\circ$$
$$2x = 116^\circ$$
$$x = \frac{116^\circ}{2} = 58^\circ$$

Answer:

$58^\circ$