How to Find Complementary and Supplementary Angles

In this article, we will introduce you to the rules of complementary and supplementary angles and how to use them to find the value of a missing angle.

Definition of the Complementary and supplementary angles

• Two angles with a sum of 90 degrees are called complementary angles.
• Two angles with a sum of 180 degrees are Supplementary angles.

Examples

Complementary and supplementary angles – Example 1:

Find the missing angle.

Solution:

Notice that the two angles form a right angle. This means that the angles are complementary, and their sum is 90.
Then: $$18+x=90→x=90^\circ-18^\circ=72^\circ$$ The missing angle is 72 degrees

Complementary and supplementary angles – Example 2:

Angles Q and S are supplementary. What is the measure of angle Q if angle S is 35 degrees?

Solution:

Q and S are supplementary $$→Q+S=180→Q+35=180→ Q =180-35=145$$

Complementary and supplementary angles – Example 3:

Find the missing angle.

Solution:

Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of $$180^\circ$$.
$$x+43=180→x=180-43=137^\circ$$

Complementary and supplementary angles – Example 4:

Find the missing angle.

Solution:

Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of $$180^\circ$$.
$$x+38=180→x=180-38=142^\circ$$

Exercises for Complementary and supplementary angles

Find the missing measurement in the pair of angles.

Find the missing measurement in the pair of angles.

1. $$\color{blue}{x=}$$

2.$$\color{blue}{x=}$$

3.$$\color{blue}{x=}$$

4.$$\color{blue}{x=}$$

5.The measure of an angle is $$31^°$$. What is the measure of its complementary angle? __________

6.The measure of an angle is $$76^°$$. What is the measure of its supplementary angle? __________

1. $$\color{blue}{156^\circ}$$
2. $$\color{blue}{15^\circ}$$
3. $$\color{blue}{113^\circ}$$
4. $$\color{blue}{46^\circ}$$
5. $$\color{blue}{59^\circ}$$
6. $$\color{blue}{104^\circ}$$

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