Chapter 2.4, Problem 15PSB

To determine

To calculate: measure of $\angle PQS$

Answer to Problem 15PSB

  ${61}^{\circ }$

Explanation of Solution

Given information: $PQ\perp QR,\angle PQS={(x^2+12)}^{\circ },\angle SQR={(43-2x)}^{\circ }$

Formula Used: Quadratic formula.

Calculation:

  $\begin{array}{l}PQ\perp QR,hence\angle PQR={90}^{\circ }\\ \therefore \angle PQS+\angle SQR={90}^{\circ }\\ \Rightarrow x^2+12+43-2x={90}^{\circ }\\ \Rightarrow x^2-2x-35=0\end{array}$

Use Quadratic formula,

  $\begin{array}{l}\therefore x=\frac{2\pm \sqrt{4+140}}{2}\\ x=\frac{2\pm 12}{2}\end{array}$

  $\therefore$ x=7 or x=-5

Rejecting negative sign, take $x=7^{\circ }$

  $\begin{array}{l}\therefore \angle PQS=x^2+12\\ =49+12\\ ={61}^{\circ }\end{array}$