Question

abcd. what is the measure of ∠c? a. 120° b. 115° c. 105° d. 100° e. 80°

Explanation:

Step1: Recall sum of interior angles of quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Set up equation

Let $\angle C=x$. Then $100^{\circ}+65^{\circ}+75^{\circ}+x = 360^{\circ}$.

Step3: Simplify left - hand side

$100 + 65+75+x=(100 + 65+75)+x=240 + x$.

Step4: Solve for $x$

$240+x = 360$, so $x=360 - 240=120^{\circ}$.

Answer:

A. $120^{\circ}$