Two angles are called complementary angles, if the sum of the degree measures of the two angles is 90.

Let us discuss complementary angles with the above figure.

In the above figure, we see angle ABC is a right angle. The right angle is formed at the Vertex B.

A ray BD divides the right angle formed at vertex B into two parts.

One part, angle ABD in the figure above, measures x degrees, while the other part, angle CBD, measures the remaining part 90^{0} – x.

The two angles, angle ABD and angle CBD are therefore called complementary angles, because the sum of the degree measures of the two angles is 90.

If two angles are complementary angles, then one of the two angles can be taken as x, and the other angle, as 90^{0} – x.

Each angle is described as the complement of the other.

So, if x is an angle, its complement is 90^{0} – x.

Let us acquire some practice with a few questions on complementary angles:

**EXAMPLE 1: **

Write the complementary angles of the following angle measures

1. 30^{0} 2. 40^{0} 3. 60^{0} 4. 80^{0}

**Answer: **

The complement of an angle x degrees is 90^{0} – x

So,

1. the complement of 30^{0} is 90^{0} – 30^{0} = 60^{0}

2. the complement of 40^{0} is 90^{0} – 40^{0} = 50^{0}

3. the complement of 60^{0} is 90^{0} – 60^{0} = 30^{0}

4. the complement of 80^{0} is 90^{0} – 80^{0} = 10^{0}

** EXAMPLE 2: **

For what degree measure of an angle, is its complement same as itself?

**Answer: **

Let the degree measure of the angle be x.

Then the complementary angle of x is 90^{0} – x

Since the angle = its own complement, so

x = 90^{0} – x, i.e. 2x = 90^{0}, so, x = 45^{0}

A Note:

In a right angled triangle, one angle is, of course, 90^{0}.

Therefore, the other two angles in a right angled triangle are complementary angles.

**right angle.**

** straight angle. **