Question

an angle is 2/3 of its complement.what is its magnitude

Answer 1

Let the angle be a

Complement angle = 90 - a

According to question,

2/3 (90 - a) = a

=> 180 - 2a = 3a

=> 5a =180

=> a = 36

Required angle = 36°

Answer 2

Let the required angle be x

Then its complement will be 90 - x

Given that, $\frac{x}{90 \: - \: x}$ = $\dfrac{2}{3}$


3x = 2 × 90 - x

3x = 180 - 2x

3x + 2x = 180

5x = 180

x = $\frac{180}{5}$

x = 36



$\therefore{}$ Its complementary angle => 90 - x => 90 - 36 => 54