When the sum of the measures of two angles is 180°, such angles are called **supplementary angles** and each of them is called a supplement of the other.

The vertices of two angles may be same or different. In the given figure ∠AOC and ∠BOC are supplementary angles as ∠AOC + ∠BOC = 180°.

Again, ∠QPR and ∠EDF are supplementary angles as ∠QPR + ∠EDF = 130° + 50° = 180°.

Angles of 60° and 120° are supplementary angles.

The supplement of an angle of 110° is the angle of 70° and the supplement of an angle of 70° is the angle of 110°

**Observations: **

(i) Two acute angles cannot be supplement of each other.

(ii) Two right angles are always supplementary.

(iii) Two obtuse angles cannot be supplement of each other.

** Worked-out Problems on Supplementary Angles:**

**1. ** Verify if 115°, 65° are a pair of supplementary angles.

**Solution: **

115° + 65° = 180°

Hence, they are a pair of supplementary angles.

**2. ** Find the supplement of the angle (20 + y)°.

**Solution: **

Supplement of the angle (20 + y)° = 180° - (20 + y)°

= 180° - 20° - y°

= (160 - y) °

**3. ** If angles of measures (x — 2)° and (2x + 5)° are a pair of supplementary angles. Find the measures.

**Solution: **

Since (x - 2)° and (2x + 5)° represent a pair of supplementary angles, then their sum must be equal to 180°.

Therefore, (x - 2) + (2x + 5) = 180

x - 2 + 2x + 5 = 180

x + 2x - 2 + 5 = 180

3x + 3 = 180

3x + 3 – 3 = 180 — 3

3x = 180 — 3

3x = 177

x = 177/3

x = 59°

Therefore, we know the value of x = 59°, put the value in place of x

x - 2

= 59 - 2

= 57°

And again, 2x + 5

= 2 × 59 + 5

= 118 + 5

= 123°

Therefore, the two supplementary angles are 57° and 123°.

**4. **Two supplementary angles are in the ratio 7 : 8. Find the measure of the angles. **Solution: **

Let the common ratio be x.

If one angle is 7x, then the other angle is 8x.

Therefore, 7x + 8x = 180

15x = 180

x = 180/15

x = 12

Put the value of x = 12

One angle is 7x

= 7 × 12

= 84°

And the other angle is 8x

= 8 × 12

= 96°

Therefore, the two supplementary angles are 84° and 96°.

**5. **In the given figure find the measure of the unknown angle.

**Solution: **

x + 55° + 40° = 180°

The sum of angles at a point on a line on one side of it is 180°

Therefore, x + 95° = 180°

x + 95° - 95° = 180° - 95°

x = 85°

● Lines and Angles

**Fundamental Geometrical Concepts**

**Some Geometric Terms and Results**

**Complementary and Supplementary Angles**

**Parallel and Transversal Lines**

**8th Grade Math Practice**** ****From Supplementary Angles to HOME PAGE**

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