Question

the quadrilateral shown is a rectangle. what is m∠mjn? a 24° b 31° c 66° d 90°

Explanation:

Step1: Recall rectangle properties

In rectangle $JKLM$, diagonals $JL$ and $KM$ are equal and bisect each other, i.e., $JN = KN$. So, $\angle JKN=\angle KJN = 24^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle JKN$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle JNK = x$. Then $x+24^{\circ}+24^{\circ}=180^{\circ}$. Solving for $x$, we get $x = 180^{\circ}- 48^{\circ}=132^{\circ}$.

Step3: Find $\angle MUN$

$\angle MUN$ and $\angle JNK$ are vertical - angles. Vertical angles are equal. So, $\angle MUN=\angle JNK$. Also, $\angle MUN = 180^{\circ}-\angle JNK$ (linear - pair). Since $\angle JNK = 132^{\circ}$, then $\angle MUN=66^{\circ}$.

Answer:

C. $66^{\circ}$