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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

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