Question

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

Answer 1

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°.