∠A and \angle B∠B are complementary angles. If m\angle A=(3x+9)^{\circ}∠A=(3x+9) ∘ and m\angle B=(x-11)^{\circ}∠B=(x−11) ∘ , then find the measure of \angle A∠A.

Answer 1

The two angles are complementary so m<A + m<B = 90

we are given m<A = 3x + 9 and m<B = x - 11

substituting we get 3x + 9 + x - 11 = 90

4x - 2 = 90

4x = 92

x = 23

m<A = 3x + 9 = 3(23) + 9 = 78