Before we solve the worked-out problems on complementary and supplementary angles we will recall the definition of complementary angles and supplementary angles.

**Complementary Angles:**

Two angles are called complementary angles, if their sum is one right angle i.e. 90°.

Each angle is called the complement of the other.

Example, 20° and 70° are complementary angles, because 20° + 70° = 90°.

Clearly, 20° is the complement of 70° and 70° is the complement of 20°.

Thus, the complement of angle 53° = 90° - 53° = 37°.

**Supplementary Angles:**

Two angles are called supplementary angles, if their sum is two right angles i.e. 180°.

Each angle is called the supplement of the other.

Example, 30° and 150° are supplementary angles, because 30° + 150° = 180°.

Clearly, 30° is the supplement of 150° and 150° is the supplement of 30°.

Thus, the supplement of angle 105° = 180° - 105° = 75°.

**Solved problems on complementary and supplementary angles: **

**1. ** Find the complement of the angle 2/3 of 90°.

**Solution: **

Convert 2/3 of 90°

2/3 × 90° = 60°

Complement of 60° = 90° - 60° = 30°

Therefore, complement of the angle 2/3 of 90° = 30°

**2. ** Find the supplement of the angle 4/5 of 90°.

**Solution: **

Convert 4/5 of 90°

4/5 × 90° = 72°

Supplement of 72° = 180° - 72° = 108°

Therefore, supplement of the angle 4/5 of 90° = 108°

**3. ** The measure of two complementary angles are (2x - 7)° and (x + 4)°. Find the value of x.

**Solution: **

According to the problem, (2x - 7)° and (x + 4)°, are complementary angles’ so we get;

(2x - 7)° + (x + 4)° = 90°

or, 2x - 7° + x + 4° = 90°

or, 2x + x - 7° + 4° = 90°

or, 3x - 3° = 90°

or, 3x - 3° + 3° = 90° + 3°

or, 3x = 93°

or, x = 93°/3°

or, x = 31°

Therefore, the value of x = 31°.

**4. ** The measure of two supplementary angles are (3x + 15)° and (2x + 5)°. Find the value of x.

**Solution: **

According to the problem, (3x + 15)° and (2x + 5)°, are complementary angles’ so we get;

(3x + 15)° + (2x + 5)° = 180°

or, 3x + 15° + 2x + 5° = 180°

or, 3x + 2x + 15° + 5° = 180°

or, 5x + 20° = 180°

or, 5x + 20° - 20° = 180° - 20°

or, 5x = 160°

or, x = 160°/5°

or, x = 32°

Therefore, the value of x = 32°.

**5. ** The difference between the two complementary angles is 180°. Find the measure of the angle.

**Solution: **

Let one angle be of measure x°.

Then complement of x° = (90 - x)

Difference = 18°

Therefore, (90° - x) – x = 18°

or, 90° - 2x = 18°

or, 90° - 90° - 2x = 18° - 90°

or, -2x = -72°

or, x = 72°/2°

or, x = 36°

Also, 90° - x

= 90° - 36°

= 54°.

Therefore, the two angles are 36°, 54°.

**6. ** POQ is a straight line and OS stands on PQ. Find the value of x and the measure of ∠ POS, ∠ SOR and ∠ ROQ.

**Solution: **

POQ is a straight line.

Therefore, ∠POS + ∠SOR + ∠ROQ = 180°

or, (5x + 4°) + (x - 2°) + (3x + 7°) = 180°

or, 5x + 4° + x - 2° + 3x + 7° = 180°

or, 5x + x + 3x + 4° - 2° + 7° = 180°

or, 9x + 9° = 180°

or, 9x + 9° - 9° = 180° - 9°

or, 9x = 171°

or, x = 171/9

or, x = 19°

Put the value of x = 19°

Therefore, x - 2

= 19 - 2

= 17°

Again, 3x + 7

= 3 × 19° + 7°

= 570 + 7°

= 64°

And again, 5x + 4

= 5 × 19° + 4°

= 95° + 4°

= 99°

Therefore, the measure of the three angles is 17°, 64°, 99°.

These are the above solved examples on complementary and supplementary angles explained step-by-step with detailed explanation.

●** Lines and Angles**

**Fundamental Geometrical Concepts**

**Some Geometric Terms and Results**

**Complementary and Supplementary Angles**

**Parallel and Transversal Lines**

**7th Grade Math Problems ****8th Grade Math Practice**** ****From Complementary and Supplementary Angles to HOME PAGE**

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