Question

∠A and \ angle B∠B are complementary angles. If m\angle A=(x+8)^{\circ}∠A=(x+8) ∘ and m\angle B=(8x+1)^{\circ}∠B=(8x+1) ∘ , then find the measure of \angle A∠A.

Answer 1

Answer: $17^{\circ}$

Step-by-step explanation:

Given

$\angle A=(x+8)^{\circ}$

$\angle B=(8x+1)^{\circ}$

Angle A and B are complementary i.e. sum of the two must be $90^{\circ}$

$\Rightarrow \angle A+\angle B=90^{\circ}\\\Rightarrow x+8+8x+1=90^{\circ}\\\Rightarrow 9x=90-9=81^{\circ}\\\Rightarrow x=9^{\circ}$

$\therefore \angle A=x+8^{\circ}=9+8\\\Rightarrow \angle A=17^{\circ}$