Exercise 53 Page 462

Let's begin with finding the value of x. Then we will use it to calculate the value of y.

Value of x

In order to find the value of x, we need to analyze the given diagram. What is the relationship between the angles measuring x^(∘) and 115^(∘)?

These are consecutive interior angles. The Consecutive Interior Angles Theorem tells us that consecutive interior angles formed by parallel lines and a transversal are supplementary. Therefore, these angles are supplementary and the sum of their measures is 180^(∘).

115+x=180 ⇒ x=65

Value of y

Before we find the value of y, we will first evaluate x+24 by substituting x= 65.

(x+24)

Substitute

x= 65

( 65+24)

AddTerms

Add terms

89

Let's show this angle on the diagram.

Notice that (2y-56)^(∘) and 89^(∘) form a linear pair, so they are supplementary. (2y-56)+89=180 To find the value of y, we will solve this equation.

(2y-56)+89=180

▼

Solve for y

RemovePar

Remove parentheses

2y-56+89=180

AddTerms

Add terms

2y+33=180

SubEqn

LHS-33=RHS-33

2y=147

DivEqn

.LHS /2.=.RHS /2.

y=73.5