Chapter 12.1, Problem 52E

To determine

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

Answer to Problem 52E

  $x={26}^0$ and $y={64}^0$ .

Explanation of Solution

Given:

  

Concept used:

The acute of a right triangle are complementary to each other.

Both angle other than ${90}^0$ are acute angle sum of two acute angle is also ${90}^0$ .

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

If two parallel lines are cut by transversal then the alternative interior angles are congruent and the pair of consecutive interior angles are supplementary.

Calculation:

The acute of a right triangle are complementary:

Sum of complementary will be ${90}^0$ .

  $\begin{array}{l}{x}^0+{64}^0={90}^0.\\ x={26}^0.\end{array}$

If two parallel lines are cut by transversal then the alternative interior angles are congruent and the pair of consecutive interior angles are supplementary.

  $\begin{array}{l}{x}^0+y^0={90}^0.\\ 26+y=90.\\ y=64.\end{array}$

Hence, $x={26}^0$ and $y={64}^0$ .