Question

incorrect your answer is incorrect. - ( mangle 1 ): your answer is incorrect. - ( mangle 2 ): your answer is incorrect. - ( mangle 3 ): your answer is incorrect. - ( mangle 4 ): your answer is incorrect. for the rhombus below, find the measures of ( angle 1 ), ( angle 2 ), ( angle 3 ), and ( angle 4 ). ( mangle 1 = 57^circ ) ( mangle 2 = 33^circ ) ( mangle 3 = 33^circ ) ( mangle 4 = 57^circ )

Explanation:

Step1: Recall rhombus angle properties

In a rhombus, opposite angles are equal, and consecutive angles are supplementary. Also, the diagonals bisect the angles. The given angle is $57^\circ$, so its opposite angle is also $57^\circ$. The consecutive angles are $180^\circ - 57^\circ = 123^\circ$.

Step2: Find $m\angle1$

The diagonal bisects the $57^\circ$ angle, so $m\angle1 = \frac{57^\circ}{2} = 28.5^\circ$

Step3: Find $m\angle3$

$\angle3$ is in the consecutive angle pair. The diagonal bisects the $123^\circ$ angle, so $m\angle3 = \frac{123^\circ}{2} = 61.5^\circ$

Step4: Find $m\angle2$

$\angle2$ is equal to $\angle1$ (alternate interior angles from parallel sides of rhombus), so $m\angle2 = 28.5^\circ$

Step5: Find $m\angle4$

$\angle4$ is equal to $\angle3$ (alternate interior angles from parallel sides of rhombus), so $m\angle4 = 61.5^\circ$

Answer:

$m\angle1 = 28.5^\circ$
$m\angle2 = 28.5^\circ$
$m\angle3 = 61.5^\circ$
$m\angle4 = 61.5^\circ$