Question

find the measure of the numbered angles in the rhombus. the diagram is not drawn to scale. m∠1 = 90°, m∠2 = 41° and m∠3 = 41° m∠1 = 90°, m∠2 = 41° and m∠3 = 69.5° m∠1 = 90°, m∠2 = 41° and m∠3 = 49° m∠1 = 90°, m∠2 = 49° and m∠3 = 41°

Explanation:

Step1: Recall rhombus properties

The diagonals of a rhombus are perpendicular to each other. So, $m\angle1=90^{\circ}$.

Step2: Use angle - congruence property

The diagonals of a rhombus bisect the angles of the rhombus. So, $m\angle2 = 41^{\circ}$ as the given angle and $\angle2$ are congruent due to diagonal - angle - bisecting property.

Step3: Calculate $\angle3$

In the right - triangle formed by the diagonals, we know that the sum of the interior angles of a triangle is $180^{\circ}$. In the right - triangle with $\angle1 = 90^{\circ}$ and $\angle2=41^{\circ}$, we use the formula $m\angle1 + m\angle2+m\angle3=180^{\circ}$. Substituting the values, we get $90^{\circ}+41^{\circ}+m\angle3 = 180^{\circ}$. Then $m\angle3=180^{\circ}-(90^{\circ} + 41^{\circ})=49^{\circ}$.

Answer:

C. $m\angle1 = 90^{\circ},m\angle2 = 41^{\circ}$ and $m\angle3 = 49^{\circ}$