# Two Complementary Angles Are Such that Two Times the Measure of One is Equal to Three Times the Measure of the Other. the Measure of the Smaller Angle is - Mathematics

MCQ

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is

#### Options

• 45°

• 30°

• 36°

•  none of these

#### Solution

Let one angle be x°.

Then, the other complementary angle becomes (90 - x)°

It is given that two times the angle measuring x°is equal to three times the angle measuring (90 - x)°

Or, we can say that:

2x = 3(90 - x)

2x = 270 - 3x

2x + 3x = 270

5x = 270

On dividing both sides of the equation by 5,we get

x = 270/5

x = 54

Also, the other complementary angle becomes

90 - x = 90 - 54

= 36

Thus, the measure of the required smaller angle is 36°.

Concept: Introduction to Lines and Angles
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Chapter 10: Lines and Angles - Exercise 10.6 [Page 56]

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.6 | Q 25 | Page 56
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