Question

if $overline{hk}congoverline{jk}$ and $mangle hik = 44^{circ}$, what is $mangle hij$?
$mangle hij=square^{circ}$

Explanation:

Step1: Identify congruent right - triangles

Since $\overline{HK}\cong\overline{JK}$ and $\angle J = \angle H=90^{\circ}$, and $\overline{IK}=\overline{IK}$ (common side), right - triangles $\triangle HIK$ and $\triangle JIK$ are congruent by the Hypotenuse - Leg (HL) congruence theorem.

Step2: Find the measure of $\angle HIK$ and $\angle JIK$

Because $\triangle HIK\cong\triangle JIK$, $\angle HIK=\angle JIK$. Given that $m\angle HIK = 44^{\circ}$, then $m\angle JIK = 44^{\circ}$.

Step3: Calculate $m\angle HIJ$

$m\angle HIJ=m\angle HIK + m\angle JIK$. So $m\angle HIJ=44^{\circ}+44^{\circ}=88^{\circ}$.

Answer:

$88$