Chapter 1, Problem 10CR

To determine

To find the values of x and the angles in the polygon.

Answer to Problem 10CR

  $x=10°$

Angles: $110°,50°\text{ and 20}°.$

Explanation of Solution

Given:

  

Formula used:

Sum of the angles in a triangle is $180°.$

Calculation:

From the given figure, Sum of the angles in a triangle is $180°$

Given that the angles are $110°,5x°\text{ and 2}x°.$

  $\begin{array}{l}\text{Sum of the angles in a triangle}=180°\\ \Rightarrow 110+5x+2x=180\\ \Rightarrow 110+7x=180\\ \Rightarrow 7x=180-110\\ \Rightarrow 7x=70\\ \Rightarrow x=10\end{array}$

Therefore, the angles are,

  $\begin{array}{c}\Rightarrow 5x=5\times 10=50°\\ \Rightarrow 2x=2\times 10=20°\end{array}$

Conclusion:

Therefore, $x=10°$ and the angles of the polygon are $110°,50°\text{ and 20}°.$