Supplementary angles. They both add up to equal 180 degrees
Given

we have

Squaring both sides, we have

And finally

Note that, when we square both sides, we have to assume that

because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose

and you'll have

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

and you'll have

Squaring both sides (and here's the mistake!!) you'd have

which is not a solution for the equation, if we plug it in we have

Which is clearly false
START WITH 1 COUNT BY ONES 1, 2, 3, 4, 5, 6
START WITH 8 COUNT BY ONES 8, 9, 10, 11, 12, 13
Refer to the edited figure.
Triangles ABC and A'B'C' are similar because of AAA.
Also,

Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.
Yes, it is.
2(3) - 3(2) = 0
2(3) + 2 = 8