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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

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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

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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
  Is there an error in this question or solution?

APPEARS IN

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