Exercise 3 Page 537

Note that two of the lines are parallel.

x=5 (Alternate Interior Angles Theorem)
y=13 (Consecutive Interior Angles Theorem)

Practice makes perfect

Examining the figure, we see that 42^(∘) and (8x+2)^(∘) are alternate interior angles. Therefore, by the Alternate Interior Angles Theorem, we know that these angles are congruent. 8x+2=42 Let's solve this equation.

8 x + 2 = 42

SubEqn

LHS-2=RHS-2

8 x = 40

DivEqn

.LHS /8.=.RHS /8.

x = 5

To find y, we use that 42^(∘) and [6(2y-3)]^(∘) are consecutive interior angles. By the Consecutive Interior Angles Theorem, these angles are supplementary. 6(2y-3)+42=180 Let's solve this equation.

6(2y-3)+42=180

Distr

Distribute 6

12y-18+42=180

AddTerms

Add terms

12+24=180

SubEqn

LHS-24=RHS-24

12y=156

DivEqn

.LHS /12.=.RHS /12.