Question

find the measure of the numbered angles in each rhombus.
m∠1 = 22°
m∠2 = 22°
m∠3 = \square°

Explanation:

Step1: Recall rhombus angle properties

Adjacent rhombus angles are supplementary: $180^\circ - 136^\circ = 44^\circ$.

Step2: Use diagonal angle bisector rule

The diagonal bisects the $44^\circ$ angle: $\frac{44^\circ}{2} = 22^\circ$, so $\angle 3 = 22^\circ$.
(Alternatively, opposite rhombus angles are equal, so the angle opposite $136^\circ$ is $136^\circ$, and the triangle formed by the diagonal has angles summing to $180^\circ$: $180^\circ - 136^\circ - 22^\circ = 22^\circ$)

Answer:

$22$