Chapter 12, Problem 18CP

To determine

To find: The value of $x$ .

Answer to Problem 18CP

The value of $x$ is ${145}^{\circ }$ .

Explanation of Solution

Given information : Interior angle of the triangle is right angle and one exterior angle is ${125}^{\circ }$ .

Concept used : The sum of the angles of a triangle is ${180}^{\circ }$ and the value of a straight angle is ${90}^{\circ }$ .

The value of the interior angle to the vertex where exterior angle is ${125}^{\circ }$ .

So, the value interior angle on this vertex is $\left(180-{125}^{\circ }\right)={55}^{\circ }$ , because they are straight angle.

And the third angle of the triangle is $\left\{{180}^{\circ }-\left({55}^{\circ }+{90}^{\circ }\right)\right\}=\left({180}^{\circ }-{145}^{\circ }\right)={35}^{\circ }$

According to the problem, they are the straight angles.

  $\begin{array}{l}\left({35}^{\circ }+x\right)={180}^{\circ }\\ \Rightarrow x={180}^{\circ }-{35}^{\circ }\\ \Rightarrow x={145}^{\circ }\end{array}$