Find the angles in each of the following.

The angles whose supplement is four times its complement.

Let the compliment of an angle be x°

According to the question,

Supplement of the angle = 4x°

We know that two angles are said to be supple mentary if their sum is 180°.

So, required angle = 180° - 4x° ..(I)

Also, if the two angles are complimentary their sum is 90°.

⇒ required angle = 90° - x° …(II)

Equating I and II,

90° - x° = 180° - 4x°

⇒ 3x° = 90°

⇒ x° = 30°

Hence, required angle = 90° - x° = 90° - 30° = 60°