Question

given the diagram below, what is m∠d? a. 108° b. 68° c. 74° d. 72°

Explanation:

Step1: Recall sum of angles in a quadrilateral

The sum of interior - angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up an equation

Let $m\angle D=x$. We know that $m\angle A = 72^{\circ}$, $m\angle B=108^{\circ}$, and $m\angle C = 108^{\circ}$. So, $72^{\circ}+108^{\circ}+108^{\circ}+x=360^{\circ}$.

Step3: Solve the equation

First, add the known angles: $72^{\circ}+108^{\circ}+108^{\circ}=288^{\circ}$. Then, $x=360^{\circ}-288^{\circ}=72^{\circ}$.

Answer:

D. $72^{\circ}$