Question

quadrilateral hijk is a rhombus. what is $m\angle hjk$?
$m\angle hjk = \square ^\circ$
the angle at $i$ is $56^\circ$

Explanation:

Step1: Recall rhombus side property

In rhombus $HIJK$, $HJ = IJ$, so $\triangle HJI$ is isosceles.

Step2: Find $\angle JHI$

$\angle JHI = \angle JIH = 56^\circ$

Step3: Calculate $\angle HJI$

Sum of angles in a triangle is $180^\circ$.
$\angle HJI = 180^\circ - 56^\circ - 56^\circ = 68^\circ$

Step4: Recall rhombus adjacent angle property

Adjacent angles in a rhombus are supplementary. Let $\angle HJK = x$, then $x + \angle HJI = 180^\circ$

Step5: Solve for $\angle HJK$

$x = 180^\circ - 68^\circ = 112^\circ$

Answer:

$112$