Question

Given m
||n, find the value of x and y.
(3y+8) (9x+1)°
(x+19)°
m
n

Answer 1

x = 16 , y = 9

Explanation:

(x + 19) and (9x + 1) are same- side exterior angles and sum to 180° , that is

x + 19 + 9x + 1 = 180

10x + 20 = 180 ( subtract 20 from both sides )

10x = 160 ( divide both sides by 10 )

x = 16

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9x + 1 = 9(16) + 1 = 144 + 1 = 145

9x + 1 and 3y + 8 are a linear pair and sum to 180° , then

3y + 8 + 145 = 180

3y + 153 = 180 ( subtract 153 from both sides )

3y = 27 ( divide both sides by 3 )

y = 9

Answer 2

x = 16

y = 9

Explanation:

Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)

So the two angles add up to 180°

x+19 + 9x + 1 = 180°

combine like terms

10x + 20 = 180

subtract 20

10x = 160

divide by 10

x = 16

Now you can find the measure of the angle marked 9x+1.

9(16) + 1

= 144 + 1

= 145

Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°

3y + 8 + 145 = 180

combine like terms

3y + 153 = 180

subtract 153

3y = 27

divide by 3

y = 9