Chapter 3.2, Problem 29PPS

To determine

To determine the value of variable.

Answer to Problem 29PPS

  $\begin{array}{l}x={60}^{\circ }\\ y={10}^{\circ }\end{array}$

Explanation of Solution

Given information :

  

From the given figure we can say that $x+{120}^{\circ }={180}^{\circ }$ or $x={60}^{\circ }$

Given angles are supplementary by consecutive interior angles theorem.

Now ${\left(3y+40\right)}^{\circ }+{\left(3x-70\right)}^{\circ }={180}^{\circ }$

(Both angles are supplementary as they lie on a straight line)

Hence we get,

  $\begin{array}{l}{\left(3y+40\right)}^{\circ }+{\left(3x-70\right)}^{\circ }={180}^{\circ }\\ 3x+3y={180}^{\circ }-{40}^{\circ }+{70}^{\circ }\\ x+y=\frac{{210}^{\circ }}{3}\\ x+y={70}^{\circ }\end{array}$

Now put $x={60}^{\circ }$ we get,

  $y={10}^{\circ }$