Essentially, what we're looking at here are two alternate interior angles.
Wait. What? Alternate interior angles?
It sounds like some super fancy math jargon, but it's a fairly simple concept that I'll try my best to explain. First, let's look at lines L and M as two parallel lines, meaning that these two are lines with equal slopes, and will never intersect. See that line that goes in between the parallel lines L and M? That's called a transversal. It's basically a line that goes through two parallel lines.
Now we know that there's a transversal going through the parallel lines. So what? Well, there's a couple of special attributes to transversals. See the two angles, 7x-7 and 4x+14? As you can tell, these two angles alternate in the interior space between the transversal and the parallel lines.
Alternate interior angles are equal. There's a way to prove that they're equal, but I won't bore you with the specifics since that's not what the question's asking.
If the angles need to be equal for lines L and M to be parallel, we can make an equation that'll solve for x:
7x - 7 = 4x + 14
Subtract 4x from both sides:
7x - 4 x - 7 = 4x - 4x + 14
3x - 7 = 14
Add 7 to both sides:
3x - 7 + 7 = 14 + 7
3x = 21
Divide both sides by 3 to completely isolate x:
[tex]\frac{3x}{3}[/tex] = [tex]\frac{21}{3}[/tex]
x = 7
And that's our answer! If you need me to explain anything any further, just ask!
- breezyツ
