Question

find angle whose complement is one third of its supplent

Answer 1

$\textbf{Hello Mate!}$

Let an angle be x

Then, its complement = 90° - x

And its supplement = 180° - x

Equation :-

90° - x = 1 / 3 ( 180° - x )

90° - x = 60° - x / 3

90° - 60° = - x / 3 + x

30° = ( - x + 3x ) / 3

30° × 3 / 2 = x

So value of x = 45°

$\boxed{Answer: \:value\:of \:x\: = 45°}$

Hope it helps

Answer 2

Answer:

Consider the required angle as x°

We know that the complement can be written as 90° – x°

and the supplement can be written as 180° – x°

90° – x° = 1/3(180° – x°)

We can also write it as

90° – x° = 60° – (1/3) x°

So we get

x° – (1/3)x° = 90° – 60°

(2/3) x° = 30°

By division we get

x° = ((30×3)/2)

x° = 45°

Therefore, the angle whose complement is one third of its supplement is 45°.