Question

If m<1=7x and m<2=5x+30 lines m and n are parallel when x equals
1) 12.5
2) 87.5
3) 15
4) 105
(explain)

Answer 1

is that a less than or angle?

Answer 2

m and n are parallel if 1 and 2 are equal

Answer 3

http://www.mathsisfun.com/geometry/alternate-interior-angles.html

Answer 4

m<1 and m<2 forms alternate interior angles. they are same

Answer 5

that is cute to know, but solving for x is what proves angle 1 and angle 2 are the same

Answer 6

we are given

y = 7x
y = 5x + 30
from the looks of the equation, our slopes are not equal. well we can easily spot that, but we have to make it equal and that is the point of this exercise.
so, we do the following:

-7x + y = 0 (eq 1)
-5x + y = 30 (eq 2)

if we multiply eq 1 by -1 y becomes negative and then x becomes positive

7x - y = 0
-5x + y = 30
--------------
2x = 30

x = 15

Answer 7

(eq 1) y = 7*15 = 105

(eq 2) y = 5*15 + 30 = 105

105 = 105