A ∠A and ∠ B ∠B are complementary angles. If m ∠ A = ( 3 x − 8 ) ∘ ∠A=(3x−8) ∘ and m ∠ B = ( x + 26 ) ∘ ∠B=(x+26) ∘ , then find the measure of ∠ A ∠A.

Answer 1

Complimentary angles add up to 90° if the two angles in question are ∠A and ∠B then:

∠mA + m∠B = 90°

And if the measure of ∠A = 3x - 8 and if the measure of ∠B = x + 26 then:

(3x - 8) + (x + 26) = 90

4x + 18 = 90

4x = 72

x = 18

If x = 18 and m∠A = 3x - 8 then m∠A = 3(18) - 8 = 46°