Question

for the rhombus below, find the measures of $\angle 1$, $\angle 2$, $\angle 3$, and $\angle 4$.
$m\angle 1\\ =\\ \square^{\circ}$
$m\angle 2\\ =\\ \square^{\circ}$
$m\angle 3\\ =\\ \square^{\circ}$
$m\angle 4\\ =\\ \square^{\circ}$

Explanation:

Step1: Use rhombus angle properties

In a rhombus, opposite angles are equal, and adjacent angles are supplementary. Also, the diagonal bisects the vertex angles. Given $\angle 4 = 32^\circ$, so $\angle 2 = \angle 4 = 32^\circ$.

Step2: Calculate $\angle 1$

Adjacent angles sum to $180^\circ$. So $\angle 1 = 180^\circ - 2\times32^\circ$
$\angle 1 = 180^\circ - 64^\circ = 116^\circ$

Step3: Find $\angle 3$

Opposite angles of rhombus are equal, so $\angle 3 = \angle 1 = 116^\circ$

Answer:

$m\angle 1 = 116^\circ$
$m\angle 2 = 32^\circ$
$m\angle 3 = 116^\circ$
$m\angle 4 = 32^\circ$