Question

How did my teacher get 11 for #17

Answer 1

Complementary angles mean that the sum adds up to 90 degrees.
We are given A and B are complementary, so
angle A + angle B = 90  (as stated in the solution).
Substituting angles, =>
3x-8 + 5x+10 = 90
group like terms
3x + 5x -8 +10 =90
simplify
8x + 2 =90
Subtract 2 from each side of the equal sign
8x +2 -2  =  90 -2
=>
8x = 88
divide by 8 on both sides
8x/8 = 88/8
x = 11

Substitute x=11 into angles A and B
angle A = 3x-8 = 3(11)-8 = 25 degrees
angle B = 5x+10 = 5(11)+10 = 65 degrees

Check supplementary angles
A+B = 25+65 = 90   => angles A & B are complementary, .... solution is good.

Answer 2

Complementary angles ⇒ the angles add up to 90°

∠A and ∠B are complementary ⇒ ∠A + ∠B = 90°

∠A + ∠B = 90°

Plug in the values for ∠A and ∠B:
(3x - 8) + (5x + 10)  = 90

Open the brackets:
3x - 8 + 5x + 10 = 90

Combine like terms:
8x + 2 = 90

Subtract 2 from both sides:
8x = 88

Divide both sides by 8:
x = 11

Answer: x = 11