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Question
If the supplement of an angle is two-third of itself. Determine the angle and its supplement.
Solution
Given that
Supplementary of an angle = `2/3` of angle itself.
The angle measured be ‘x’ say.
Supplementary angle of x will be (180 - x)°
It is given that
(180 - x)° = `2/3` x°
⇒ 180° - x° = `2/3` x°
⇒ `2/3` x° + x° = 180°
⇒ 2x° + 3x° = 3 × 180°
⇒ 5x° = 540°
⇒ x = 108°
Hence, supplement =180 -108 = 72°
∴ Angle will be 108° and its supplement will be 72°.
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