Chapter 7.1, Problem 18PSB

To determine

To calculate : The value of $m\angle PST$ .

Answer to Problem 18PSB

The value of $m\angle PST={105}^0$

Explanation of Solution

Given information : The following information has been given

  $\angle PST=(x+3y)$

  $\angle P={45}^0$

  $\angle R=2y$

  $\angle PSR=5x$

Formula used : All the angles of any triangle add up to ${180}^0$

Calculation : In triangle PRS, we know that $\angle P={45}^0$ . Thus, we can say that

  $\angle R+\angle PSR={180}^0-{45}^0$

Substituting the values of $\angle R=2y$ and $\angle PSR=5x$ , we get

  ${135}^0=2y+5x$

Also, we know that $\angle PST=(x+3y)$ , which is supplementary to angle S in the triangle. Thus, from them, we get

  ${180}^0=3y+6x$

From the above two equations, we can say that

  $x={15}^0$ and $y={30}^0$

Now, we substitute these values into $\angle PST=(x+3y)$

  $m\angle PST={105}^0$