Chapter 12.1, Problem 50E

To determine

To find: the value of $x$ and $y$ using mathematical connections.

Answer to Problem 50E

  $x={118}^0$ and $y={96}^0$ .

Explanation of Solution

Given:

  

Concept used:

If two parallel lines are cut by transversal then the alternative interior angles are congruent.

Sum of the three angles of triangle is always ${180}^0$ .

According to the exterior angle theorem:

The measurement of the exterior angle of a triangle is equal to the sum of the measurement of two nonadjacent interior angles.

Calculation:

If two parallel lines are cut by transversal then the alternative interior angles are congruent.

From given diagram it is clearly point out that the $x={118}^0$ .

According to the exterior angle theorem:

The measurement of the exterior angle of a triangle is equal to the sum of the measurement of two nonadjacent interior angles.

From given diagram it is clearly point out that the:

  $\begin{array}{l}{x}^0={22}^0+y^0.\\ 118=y+22.\\ y=96.\end{array}$

Hence, $x={118}^0$ and $y={96}^0$ .