Answer:
Step-by-step explanation:
#1. For lines l and m to be parallel, angles 3 and 6 would have to add up to equal 180. This is the Same Side Interior Angle Theorem.
For #2, angles 3 and 7 are corresponding, meaning they are in the same place in both angle groups. Because of this, they are congruent. That means that they equal one another.
If angle 3 is 4x + 12 and x = 15, then angle 3 = 72.
If angle 7 is 80 - x and x = 15, then angle 7 = 65. So if this is the case, the lines l and m are not parallel. In order for them to be parallel, angle 3 has to equal angle 7:
4x + 12 = 80 - x and we solve for the value of x that will make the lines parallel:
5x = 68 so
x = 13.6
