Chapter 5, Problem 16RP

To determine

To Find: The measure of angle C.

Answer to Problem 16RP

  $m\angle C=106°$

Explanation of Solution

Given:

A parallelogram.

  

  $\angle A=\left(2x+6\right)°\text{and }\angle B=\left(x+24\right)°$

Concept Used:

In parallelogram:

• Opposite angles of a parallelogram are equal.
• Adjacent angles of a parallelogram are supplementary.

Calculation:

Since, in parallelogram, adjacent angles of a parallelogram are supplementary.

  $\begin{array}{l}\Rightarrow \angle A+\angle B={180}^{\circ }\\ \Rightarrow \left(2x+6\right)°+\left(x+24\right)°=180°\\ \Rightarrow \left(3x\right)°+\left(30\right)°=180°\\ \Rightarrow \left(3x\right)°=150°\\ \Rightarrow x=50\\ \text{Since, in parallelogram opposite angles are equal}\text{.}\\ \Rightarrow \angle C=\angle A\\ \Rightarrow m\angle C=\left(2\times 50+6\right)°=106°\\ \therefore m\angle C=106°\\ \end{array}$