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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Inequalities in Two Triangles

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Exercise 54 Page 462

The angles measuring 78^(∘) and (x+36)^(∘) are consecutive interior angles.

x=66
y=35

Practice makes perfect

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+36)^(∘) and 78^(∘)?

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^(∘). 78+(x+36)=180 We can solve this equation to find the value of x.

78+(x+36)=180

▼

Solve for x

Remove parentheses

78+x+36=180

Add terms

x+114 = 180

LHS-114=RHS-114

x=66

Value of y

To find the value of y, we need to find the relationship between the angles which measure (2y)^(∘) and 110^(∘). Let's analyze the diagram once more.

Notice that they are also consecutive interior angles. 2y+110=180 To find the value of y, let's solve this equation!

2y+110=180

LHS-110=RHS-110

2y=70

.LHS /2.=.RHS /2.

y=35

Subchapter links

Exercises p.457-462