Chapter 2.5, Problem 14PSB

To determine

To calculate: measure of $\angle B$ .

Answer to Problem 14PSB

  ${57}^{\circ }$

Explanation of Solution

Given information: $\angle A$ is complimentary to $\angle B$ and $\angle C$ is complementary to $\angle B$ . $\angle A={(3x+y)}^{\circ },\angle B={(x+4y+2)}^{\circ }\angle C={(3y+3)}^{\circ }$

Calculation:

  $\angle A+\angle B={90}^{\circ }$ and $\angle B+\angle C={90}^{\circ }$

  $\therefore 3x+y+4y+2={90}^{\circ }$ And $x+4y+2+3y-3={90}^{\circ }$

  $\therefore 4x+5y={88}^{\circ }$ And $x+7y={90}^{\circ }$

Solving these equation, x=7 y=12

Hence

  $\begin{array}{l}\angle B=7+48+2\\ ={57}^{\circ }\end{array}$