Chapter 2.2, Problem 18PSB

To determine

To calculate: to find the measure of larger angle.

Answer to Problem 18PSB

  ${158}^{\circ }$

Explanation of Solution

Given information: two supplementary angles such that larger of the angles exceeds 7 times the smaller by $4^{\circ }$ .

Formula Used: sum of supplementary angles is ${180}^{\circ }$ .

Calculation: let measure of smaller angle be $x^{\circ }$ .

Then measure of larger angle is ${\left(7x+4\right)}^{\circ }$

  $\because$ These angles are supplementary

  $\begin{array}{l}$ \therefore x^{\circ }+{(7x+4)}^{\circ }={180}^{\circ }$\therefore 8x^{\circ }={176}^{\circ }\\ \therefore x^{\circ }={22}^{\circ }\end{array}$

Hence larger angle = $7\times {22}^{\circ }+4^{\circ }={158}^{\circ }$