Chapter 11, Problem 2MCQ

To determine

Tocalculate: $x,m\angle G,m\angle H$

Answer to Problem 2MCQ

  $x=91°,\angle G=102°,\angle H=78°$

Explanation of Solution

Given information: $m\angle G=x+11,m\angle H=x-13$ such that angles G and are supplementary

Formula used:If two angles are supplementary then sum of those angles is $180°$

Calculation:

As angles G and are supplementary,

  $\angle G+\angle H=180°$

Put $\angle G=x+11,\angle H=x-13$

  $\begin{array}{l}\angle G+\angle H=180°\\ \Rightarrow x+11+x-13=180°\\ \Rightarrow 2x-2=180°\\ \Rightarrow 2x=182°\\ \Rightarrow x=\frac{182}{2}\\ =91°\end{array}$

Now find $\angle G,\angle H$

  $\begin{array}{l}\angle G=91+11=102°\\ \angle H=91-13=78°\end{array}$