To find x in the first problem you would make 4x and 8x-12 equal to each other because vertical angles are congruent. x would equal 3. When you plug it in, both of the angles with x equal 12.
1) Vertical angles are equal, so we can set 4x and 8x - 12 equal to each other.
4x = 8x - 12
-4x = -12 (subtract 8x from both sides)
x = 3 (divide both sides by -4)
We can then substitute 3 in for x in 8x - 12.
8(3) - 12
12
Because adjacent angles equal 180, we can put 6y + 10 and 12 (8x - 12) into an equation like this:
6y + 10 + 12 = 180
6y + 22 = 180 Combine like terms
6y = 158 Subtract 22 from both sides
y = 26 1/3 Divide both sides by 6
2) When two parallel lines go through another line, they form equal angles. Therefore we can set 3x equal to 48.
3x = 48
x = 16
We can then substitute 16 in for x in 4x - 8.
4(16) - 8 = 56
Remember, when two parallel lines go through another line, they form equal angles. So the top angle in the smaller triangle must by 56. We know the other two angles are y^2 and 48, so we can add them all equal to 180 (the degrees in a triangle).
