Question

Two complementary angles are in the ratio 2:3 .Find the angles

Answer 1

let any no. x to be multiplied to remove ratio
therefore angles are 2x and 3x

now given that 2x + 3x = 90
5x = 90
x = 18

angles:
2x = 2×18 = 36°
3x = 3×18 = 54°.

Answer 2

Given:

Two complementary angles are in the ratio 2:3.

To find:

The angles.

Solution:

The two complementary angles are 36° and 54°.

As we know that if two angles A and B are complementary angles then their sum will be equal to 90°.

This means

angle A + angle B = 90°

Now,

as given in the question,

Two complementary angles are in the ratio 2:3.

So,

let the common ratio be x.

Thus,

Two complementary angles are in the ratio 2x and 3x.

Now,

$2x + 3x = 90°$

$5x = 90$

$x = 18$

On putting the value of x, we get

One angle = 2x = 2(18) = 36°

Another angle = 3x = 3(18) = 54°

Hence, the measure of two complementary angles is 36° and 54°.