Translate to a system of equations and solve: Two angles are complementary. One angle is 42 degrees more than one half the other. Find the angles.

llm

Answered on Sun Aug 07 2022

Two angles are complementary,

So, ∠x + ∠y= 90°…eqn¹

∠x = ∠y(½) + 42

∠x = ∠y/2 + 42 …eqn²

Let's put ∠x's value from eqn² in eqn¹

∠x + ∠y= 90°

∠y/2 +42 + ∠y= 90°

∠y/2 + ∠y= 90° -42

3∠y/2 =48

3∠y = 48*2

3∠y = 96

∠y = 32°

Now, put ∠y = 32°in eqn¹

∠x + ∠y= 90°

∠x + 32°= 90°

∠x = 90° -32°

∠x =58°