Question

Given m || n, find the value of x and y (equations in picture)

Answer 1

x = 10 , y = 29

Explanation:

The angle vertically opposite (4x - 7) is congruent , then

4x - 7 and 6x + 7 are same- side interior angles and sum to 180° , so

4x - 7 + 6x + 7 = 180

10x = 180 ( divide both sides by 10 )

x = 10

Then

6x + 7 = 6(10) + 7 = 60 + 7 = 67

3y - 20 is vertically opposite 6x + 7 and is congruent , that is

3y - 20 = 67 ( add 20 to both sides )

3y = 87 ( divide both sides by 3 )

y = 29

Answer 2

x=17.7 y=27.4

Explanation:

We should start with the equation with only 1 variable.

4x-4+6x+7= 180

Solve.

10x+3=180

10x=177

x=17.7

3y-20+4x-7 should equal 180.

So solve.

3y-27+4x=180

Substitute for x.

3y-27+4(17.7)=180

Solve.

3y-27+70.8=180

3y=82.2

y=27.4