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: Identify ∠1 property

In a rhombus, diagonals are perpendicular, so $m\angle1 = 90^\circ$.

Step2: Calculate ∠2

Rhombus angles sum to $180^\circ$ (adjacent). $\angle2 = 90^\circ - 53^\circ = 37^\circ$.

Step3: Identify ∠3 property

Opposite angles in rhombus are equal, so $m\angle3 = 53^\circ$.

Step4: Identify ∠4 property

Alternate interior angles are equal, so $m\angle4 = 37^\circ$.

Answer:

$m\angle1 = 90^\circ$
$m\angle2 = 37^\circ$
$m\angle3 = 53^\circ$
$m\angle4 = 37^\circ$