Question

for the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.

Explanation:

Step1: Identify rhombus angle properties

In a rhombus, opposite angles are equal, and adjacent angles are supplementary. The given angle is $41^\circ$, so $\angle 1 = 41^\circ$.

Step2: Calculate adjacent angle

Adjacent angles sum to $180^\circ$.
$\angle 2 = 180^\circ - 41^\circ = 139^\circ$

Step3: Use diagonal angle bisector rule

Rhombus diagonals bisect angles. $\angle 3$ is half of $\angle 2$.
$\angle 3 = \frac{139^\circ}{2} = 69.5^\circ$

Step4: Use diagonal angle bisector rule

Rhombus diagonals bisect angles. $\angle 4$ is half of $\angle 1$.
$\angle 4 = \frac{41^\circ}{2} = 20.5^\circ$

Answer:

$m\angle 1 = 41^\circ$
$m\angle 2 = 139^\circ$
$m\angle 3 = 69.5^\circ$
$m\angle 4 = 20.5^\circ$