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9. If the Complement of an Angle is Equal to the Supplement of the Thrice of It. Find the Measure of the Angle. - Mathematics

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If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle. 

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Solution

The angle measured will be ' x ' say.

Its complementary angle is (90° - x°) and

Its supplementary angle is (180° - 3x°)

Given that,

Supplementary of thrice of the angle = (180° - 3x°)

According to the given information

(90 - x)° = (180 - 3x

⇒ 3x° - x° = 180° - 90°

⇒ 2x° = 90°

⇒ x = 45°

The 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 13 | Page 7

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