Question

given the diagram below, what is m∠a?
a. 110°
b. 60°
c. 80°
d. 70°

Explanation:

Step1: Recall quadrilateral angle - sum property

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

Step2: Let $m\angle A=x$.

We know that $m\angle B = 110^{\circ}$, $m\angle C=110^{\circ}$, and $m\angle D = 70^{\circ}$. So, $x+110^{\circ}+110^{\circ}+70^{\circ}=360^{\circ}$.

Step3: Solve for $x$.

$x=360^{\circ}-(110^{\circ}+110^{\circ}+70^{\circ})=360^{\circ}-290^{\circ}=70^{\circ}$.

Answer:

D. $70^{\circ}$