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: Recall rhombus angle properties

In a rhombus, opposite angles are equal, consecutive angles are supplementary, and diagonals bisect the angles.

Step2: Calculate $m\angle 2$

Diagonal bisects the angle, so $m\angle 2 = 41^\circ$

Step3: Calculate $m\angle 3$

Consecutive angles sum to $180^\circ$. First find the full angle: $180^\circ - 2\times41^\circ = 98^\circ$, so $m\angle 3 = 98^\circ$

Step4: Calculate $m\angle 1$

Opposite angles are equal, so $m\angle 1 = m\angle 3 = 98^\circ$

Step5: Calculate $m\angle 4$

Diagonal bisects the angle equal to $\angle 3$, so $m\angle 4 = \frac{98^\circ}{2} = 49^\circ$

Answer:

$m\angle 1 = 98^\circ$
$m\angle 2 = 41^\circ$
$m\angle 3 = 98^\circ$
$m\angle 4 = 49^\circ$