Q4 of 23 Page 87

Find the angles in each of the following.

The angle whose complement is one sixth of its supplement.

Let the supplement of an angle be x°


According to the question,


Compliment of the angle


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


So, ..(I)


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


…(II)


Equating I and II,





⇒ x° = 108°


Hence, required angle = 180° - x° = 180° - 108° = 72°


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