Question

If the complement of an angle is one-third of its supplement, find the angle

Answer 1

Answer: 45°

Explanation:

Let the angle be x and its complement be y

Also,

Complement = 1/3 × Supplement

So,

Supplement = 3 × Complement

= 3y

According to Question:

I. x + y = 90° -----(1)

II. x + 3y = 180° -----(2)

On subtracting eq (1) from (2) we get

2y=90°

y=45°

Now, From eq (1)

x + y = 90°

x = 90° - 45°

x = 45°

∴ The angle is 45°