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If the Supplement of an Angle is Two-third of Itself. Determine the Angle and Its Supplement. - Mathematics

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If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

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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°.

Concept: Pairs of Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.1 | Q 10 | Page 7

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