Question

Given m || n, find the value of x and y

Answer 1

X = 15

Y = 50

(8x+12) + (2x+18) = 180 -- combine like terms

10x + 30 = 180 -- subtract 30 from both sides

-30 -30

10x = 150 -- divide by 10 on both sides

x = 15

and for y:

plug x into (8x+12)

8(15) + 12 = 3y - 18

120 + 12 = 3y - 18

132 = 3y - 18 -- add 18 to both sides

150 = 3y -- divide both sides by 3

y = 50

Answer 2

x = 15, y = 50

Explanation:

8x + 12 and 2x + 18 are same- side interior angles and sum to 180° , then

2x + 18 + 8x + 12 = 180

10x + 30 = 180 ( subtract 30 from both sides )

10x = 150 ( divide both sides by 10 )

x = 15

Then

8x + 12 = 8(15) + 12 = 120 + 12 = 132

3y - 18 and 8x + 12 are vertical angles and are congruent, so

3y - 18 = 132 ( add 18 to both sides )

3y = 150 ( divide both sides by 3 )

y = 50