Question

the quadrilateral shown is a rectangle. what is ( mangle mjn )?
a ( 24^circ )
b ( 31^circ )
c ( 66^circ )
d ( 90^circ )

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal and bisect each other, so $JN = MN$. Thus, $\triangle MJN$ is isosceles with $\angle JMN = \angle MJN$.

Step2: Find $\angle JMN$

$\angle JKM = 24^\circ$, and in rectangle $JKLM$, $JK \parallel ML$, so $\angle JKM = \angle KML = 24^\circ$ (alternate interior angles).

Step3: Calculate $\angle MJN$

In $\triangle MJN$, $\angle JNM = 180^\circ - 24^\circ = 156^\circ$ (linear pair with $\angle JNK$). The sum of angles in a triangle is $180^\circ$, so:
$$\angle MJN = \frac{180^\circ - 156^\circ}{2} = 66^\circ$$

Answer:

C. $66^\circ$