Question

question
find ( mangle hji ).
answer
attempt 1 out of 2
( mangle hji = square^circ )
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Explanation:

Step1: Identify equal sides & angles

Sides $\overline{JI}$ and $\overline{IH}$ are equal, so $\angle H = \angle J$. Wait, no: equal sides correspond to equal base angles. Wait, $\overline{JI} \cong \overline{IH}$, so the angles opposite them are equal: $\angle H$ (opposite $\overline{JI}$) and $\angle HJI$ (opposite $\overline{IH}$)? No, correction: in $\triangle HJI$, $\overline{JI} = \overline{HI}$, so the angles opposite are $\angle H$ (opposite $\overline{JI}$) and $\angle HJI$ (opposite $\overline{HI}$). Wait, no: vertex angle is $\angle H = 64^\circ$, so the base angles are $\angle HJI$ and $\angle HIJ$, which are equal.

Step2: Sum of triangle angles is $180^\circ$

Let $m\angle HJI = x$. Then $x + x + 64^\circ = 180^\circ$

Step3: Solve for $x$

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

Answer:

$58$