Question

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

Explanation:

Step1: Find angle 2

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. At point D, the exterior angle is 130°. Let angle 2 be one of the non - adjacent interior angles to this exterior angle and angle C = 70°. So, $\angle2+70^{\circ}=130^{\circ}$, then $\angle2 = 130^{\circ}-70^{\circ}=60^{\circ}$.

Step2: Find angle 1

Since angles 1 and 2 are supplementary (they form a straight - line), and the sum of supplementary angles is 180°. We know that $\angle1+\angle2 = 180^{\circ}$. Substituting $\angle2 = 60^{\circ}$ into the equation, we get $\angle1=180^{\circ}-\angle2$. So, $\angle1 = 180^{\circ}-60^{\circ}=120^{\circ}$.

Answer:

C. 120°