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If the Supplement of an Angle is Three Times Its Complement, Find the Angle. - Mathematics

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If the supplement of an angle is three times its complement, find the angle.

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Solution

Given that,

Supplementary of an angle = 3 times its complementary angle.

The angles measured will be x°

Supplementary angle of x will be 180° - x° and

The complementary angle of x will be (90° - x°).

It’s given that

Supplementary of angle = 3 times its complementary angle

180° - x° = 3(90° - x°)

⇒180° - x° = 270° - 3x°

⇒ 3x° - x° = 270° -180°

⇒ 2x° = 90°

⇒ x = 45°

∴ Angle measured is  45°.

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 14 | Page 7

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