Question

Quadrilateral ABCD is a parallelogram. Find m∠C if m∠C = 6x + 15 and m∠A = 13x − 41.

A) 117°


B) 63°


C) 153°


D) 27°

Answer 1

B) 63°

Explanation:

To find the measure of angle C, we first need to find the value of x.

Since opposite angles of a parallelogram are congruent, we can find the value of x by setting the expressions for opposite angles A and C equal to each other and solving for x:

`\begin{aligned}m \angle A&= m \angle C\\13x-41&=6x+15\\13x-41+41&=6x+15+41\\13x&=6x+56\\13x-6x&=6x+56-6x\\7x&=56\\7x/ 7&=56 / 7\\x&=8\end{aligned}`

Now that we have found the value of x, we can substitute this value into the expression for angle C:

`\begin{aligned}m \angle C&=6(8)+15\\&=48+15\\&=63^(\circ)\end{aligned}`

Therefore, the measure of angle C is 63°.