Chapter 12.1, Problem 51E

To determine

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

Answer to Problem 51E

  $x=85\text{ and }y=65$ .

Explanation of Solution

Given:

  

Concept used:

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.

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

Calculation:

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:

  $\begin{array}{l}{90}^0={25}^0+y^0.\\ 90=y+25.\\ y=65.\end{array}$ .

Similarly,

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:

  $\begin{array}{l}{x}^0=20+y^0.\\ x=65+20.\\ x=85.\end{array}$

Hence, $x=85\text{ and }y=65$ .