Question

what is the measure of ∠a? 100° 30° a. 70° b. 30° c. 50° d. 130°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let $\angle A=x$, $\angle B = 100^{\circ}$, and $\angle C=30^{\circ}$. Then $x+\angle B+\angle C = 180^{\circ}$.

Step2: Solve for $\angle A$

Substitute the values of $\angle B$ and $\angle C$ into the equation: $x + 100^{\circ}+30^{\circ}=180^{\circ}$. Simplify the left - hand side: $x+130^{\circ}=180^{\circ}$. Subtract 130° from both sides: $x=180^{\circ}-130^{\circ}=50^{\circ}$.

Answer:

C. $50^{\circ}$