Chapter 11, Problem 2MCQ

To determine

Tofind:The value of $x$ , $m\angle G$ and $m\angle H$ if $m\angle G=\left(x+11\right)°$ , $m\angle H=\left(x-13\right)°$ and $m\angle G$ and $m\angle H$ are supplementary.

Answer to Problem 2MCQ

Thevalue of $x$ , $m\angle G$ and $m\angle H$ are $91°$ , $102°$ and $78°$ , respectively.

Explanation of Solution

Given information:

The value of $m\angle G$ is $\left(x+11\right)°$ , $m\angle H$ is $\left(x-13\right)°$ and $m\angle G$ and $m\angle H$ are supplementary.

Calculation:

Two angles are defined as supplementary angles if their sum is $180°$ .

Since, $m\angle G$ and $m\angle H$ are complementary. So,

$m\angle G+m\angle H=180°$

Substitute $\left(x+11\right)°$ for $m\angle G$ and $\left(x-13\right)°$ for $m\angle H$ in the above equation.

$\begin{array}{c}\left(x+11\right)°+\left(x-13\right)°=180°\\ 2x-2°=180°\\ 2x=182°\\ x=91°\end{array}$

Calculate the value of $m\angle G$ .

$\begin{array}{c}m\angle G=\left(x+11\right)°\\ =\left(91+11\right)°\\ =102°\end{array}$

Calculate the value of $m\angle H$ .

$\begin{array}{c}m\angle H=\left(x-13\right)°\\ =\left(91-13\right)°\\ =78°\end{array}$

Therefore, the value of $x$ , $m\angle G$ and $m\angle H$ are $91°$ , $102°$ and $78°$ , respectively.