Exercise 3 Page 167

Examining the figure, we see that

4 2^{\circ}

and

(8 x + 2)^{\circ}

are alternate interior angles. Therefore, by the Alternate Interior Angles Theorem, we know that these angles are congruent.

8 x + 2 = 42

Let's solve this equation.

8 x + 2 = 42

$LHS - 2 = RHS - 2$

8 x = 40

$LHS / 8 = RHS / 8$

x = 5

To find

y,

we use that

4 2^{\circ}

and

[6 (2 y - 3)]^{\circ}

are consecutive interior angles. By the Consecutive Interior Angles Theorem, these angles are supplementary.

6 (2 y - 3) + 42 = 180

Let's solve this equation.

6 (2 y - 3) + 42 = 180

Distribute $6$

12 y - 18 + 42 = 180

Add terms

12 + 24 = 180

$LHS - 24 = RHS - 24$

12 y = 156

$LHS / 12 = RHS / 12$

y = 13