Chapter 11.1, Problem 24PPS

To determine

To calculate : value of x , $\angle 1$ and $\angle 5$

Answer to Problem 24PPS

  $\begin{array}{l}x=26°\\ \angle 1=130°\\ \angle 5=50°\end{array}$

Explanation of Solution

Given information: $\angle 1=5x°,\angle 5=(2x-2)°$

Formula used : Sum of linear pair of angles is $180°$

Calculation :

  

In the given figure, $\angle 1,\angle 5$ form a linear pair.

Also, sum of linear pair of angles is $180°$

So,

  $\angle 1+\angle 5=180°$ (Linear pair)

Put $\angle 1=5x°,\angle 5=(2x-2)°$

  $\begin{array}{l}5x°+(2x-2)°=180°\\ 7x°=180°+2°=182°\\ 7x°=182°\\ x=\frac{182}{7}=26\end{array}$

So,

  $\begin{array}{l}\angle 1=5x°=5(26°)=130°\\ \angle 5=(2x-2)°=\left[2(26)-2\right]°=50°\end{array}$