Exercise 13 Page 483

Looking at the figure, we can identify two pairs of vertical angles. The measure of each pair is given as algebraic expressions. One pair is written in terms of

x

and one pair is in terms of

y .

Vertical Angles 1 : Vertical Angles 2 : (10 x - 4)^{\circ} and 6 (x + 2)^{\circ} (18 y - 18)^{\circ} and 16 y^{\circ}

By the Vertical Angles Congruence Theorem, we know that vertical angles are congruent. Therefore, we can equate the given expressions and solve for

x

and

y .

Let's find the value of

x

first.

10 x - 4 = 6 (x + 2)

▼

Solve for

x

Distr

Distribute $6$

10 x - 4 = 6 x + 12

SubEqn

$LHS - 6 x = RHS - 6 x$

4 x - 4 = 12

AddEqn

$LHS + 4 = RHS + 4$

4 x = 16

DivEqn

$LHS / 4 = RHS / 4$

x = 4

Now let's do the same thing for

y .

18 y - 18 = 16 y

▼

Solve for

y

SubEqn

$LHS - 16 y = RHS - 16 y$

2 y - 18 = 0

AddEqn

$LHS + 18 = RHS + 18$

2 y = 18

DivEqn

$LHS / 2 = RHS / 2$

y = 9