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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Chapter Review

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Exercise 8 Page 534

116 and (6x+32) are alternate exterior angles and (6x+32) and (5y-21) are a linear pair.

y=17
x=14

Practice makes perfect

To find the measure of x, we use the fact that 116 and (6x+32) are alternate exterior angles. Since the lines that are cut by the transversal are parallel, by the Alternate Exterior Angles Theorem, we know they are congruent. 6x+32=116 Let's solve the equation for x.

6x+32=116

LHS-32=RHS-32

6x=84

.LHS /6.=.RHS /6.

x=14

We also see that (5y-21) and (6x+32) form a linear pair. Therefore, by the Linear Pair Postulate, we know that these angles are supplementary. (5y-21)+(6x+32)=180 By substituting the value for x, we can solve for y.

(5y-21)+(6x+32)=180

x= 14

(5y-21)+(6* 14+32)=180

▼

Solve for y

Remove parentheses

5y-21+6* 14+32=180

Multiply

5y-21+84+32=180

Add and subtract terms

5y+95=180

LHS-95=RHS-95

5y=85

.LHS /5.=.RHS /5.

y=17

Subchapter links

1 Pairs of Lines and Angles p.534

2 Parallel Lines and Transversals p.534

3 Proofs with Parallel Lines p.535

4 Proofs with Perpendicular Lines p.535

5 Using Parallel and Perpendicular Lines p.536