Question

what is m∠1? a. 130 b. 70 c. 60 d. 120

Explanation:

Step1: Find angle 2

Since the exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let $\angle 2$ be an interior angle of the triangle at $B$. The exterior angle at $D$ is $130^{\circ}$ and the non - adjacent interior angle at $C$ is $70^{\circ}$. So, $\angle 2+70^{\circ}=130^{\circ}$, then $\angle 2 = 130^{\circ}-70^{\circ}=60^{\circ}$.

Step2: Find angle 1

$\angle 1$ and $\angle 2$ are supplementary angles (they form a straight line), so $\angle 1+\angle 2 = 180^{\circ}$. Since $\angle 2 = 60^{\circ}$, then $\angle 1=180^{\circ}-\angle 2=180 - 60=120^{\circ}$.

Answer:

D. 120