Question

Given line l and line M are parallel. Find the value of x and y.

Answer 1

x = 4

y = 10

Explanation:

29x - 3 + 15x + 7 = 180 (Linear Pair)

44x + 4 = 180

44x + 4 = 180 - 4

44x = 176

`(44x)/(44) = (176)/(44)`

x = 4

29(4) - 3

116 - 3

113

13y - 17 = 113 (Alternate Exterior Angles Theorem)

13y - 17 + 17= 113 + 17

13y = 130

`(13y)/(13) = (130)/(13)`

y = 10

Answer 2

The value of x is 4, and the value of y is 10.

How to find the values of x and y?

First, two adjacent angles always add up to 180°, then:

(29x - 3) + (15x + 7) = 180

44x + 4 = 180

44x = 180 - 4

44x = 176

x = 176/44

x = 4

Now, if lines l and m are parallel, then the measures of (15x + 7) and (13y - 17) also should add up to 180°, then we can write:

(15x + 7) + (13y - 17) = 180

We know that x = 4, then:

15*4 + 7 + 13y - 17 = 180

13y + 50 = 180

13y = 180 - 50

13y = 130

y = 130/13 = 10