Question

find the measure of the numbered angles in each rhombus.
m∠1 = 22°
m∠2 = \square°

Explanation:

Step1: Recall rhombus angle properties

In a rhombus, consecutive angles are supplementary, so the angle adjacent to $136^\circ$ is $180^\circ - 136^\circ = 44^\circ$. Also, the diagonal of a rhombus bisects the angles.

Step2: Calculate $\boldsymbol{m\angle2}$

The triangle containing $\angle2$ has angles $136^\circ$, $\angle2$, and $\angle4$. Since the diagonal bisects the $44^\circ$ angle, $\angle2 = \frac{180^\circ - 136^\circ}{2}$
$\angle2 = \frac{44^\circ}{2} = 22^\circ$
(Note: We can also confirm $\angle3 = \angle1 = 22^\circ$, $\angle4 = \angle2 = 22^\circ$ using rhombus diagonal properties, but the question asks for $\angle2$ here.)

Answer:

$22$