Exercise 55 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 (4x)^(∘) and 72^(∘)?

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^(∘). 72+4x=180 We can solve this equation to find the value of x.

72+4x=180

SubEqn

LHS-72=RHS-72

4x=108

DivEqn

.LHS /4.=.RHS /4.

x=27

Value of y

To find the value of y, we need to find the relationship between the angle which measures (3y)^(∘) and 112^(∘). Let's analyze the diagram once more.

Notice that they are also consecutive interior angles. 3y+112=180 To find the value of y, let's solve this equation!

3y+112=180

SubEqn

LHS-112=RHS-112

3y=68

DivEqn

.LHS /3.=.RHS /3.

y= 22.66666 ...

RoundInt

Round to nearest integer

y≈ 23