Chapter 10.3, Problem 37HP

To determine

To calculate: The values of x and y in the given figure.

Answer to Problem 37HP

The values of x = ${50}^0$ , y = ${80}^0$ .

Explanation of Solution

Given information: In the given figure, two triangles given. In one triangle, the three angles given ${35}^0$ , ${95}^0$ and $x^0$ . In other triangle, the three angles given $x^0$ , $y^0$ and ${50}^0$ .

Calculation:

We know that, sum of three angles in a triangle is ${180}^0$ .

So for one triangle, we can write,

  $\begin{array}{l}35+95+x=180\\ \Rightarrow 130+x=180\\ \Rightarrow x=180-130\\ \Rightarrow x=50\end{array}$

For other triangle, we can also write,

  $\begin{array}{l}x+y+50=180\\ \Rightarrow 50+y+50=180\\ \Rightarrow y+100=180\\ \Rightarrow y=180-100\\ \Rightarrow y=80\end{array}$

  $\therefore$ The values of x = ${50}^0$ , y= ${80}^0$ .