**GSEB Solutions for Class 6 Mathematics – Types of Pair of Angles**

GSEB SolutionsMathsScience

**Exercise**

**Solution 1:**

**Solution 2:**

- 27° + 63° = 90°

If the sum of the measures of two angles is 90°, they form a pair of complementary angles.

∴27°, 63° form a pair of complementary angles. - 110°+ 70° = 180°

If the sum of the measures of two angles is 180°, they form a pair of supplementary angles.

∴110°, 70° form a pair of supplementary angles. - 7°+ 83°= 90°

If the sum of the measures of two angles is 90°, they form a pair of complementary angles.

∴7°, 83° form a pair of complementary angles. - 135°+ 45° = 180°

If the sum of the measures of two angles is 180°, they form a pair of supplementary angles.

∴135°, 45° form a pair of supplementary angles - 58°+ 32°= 90°

If the sum of the measures of two angles is 90°, they form a pair of complementary angles.

∴58°, 32° form a pair of complementary angles.

**Solution 3:**

**Solution 4:**

Given, ∠AED and ∠BED are angles of a linear pair.

m∠BED = 145°

m∠AED + m∠BED = 180°

⇒ m∠AED + 145°=180°

⇒ m∠AED =180° – 145° = 35°

m∠AEC = m∠BED = 145° ….[Vertically Opposite angles]

m∠BEC = m∠AED = 35° ….[Vertically Opposite angles]

**Solution 5:**

1. Two pairs of vertically opposite angles are formed.

2. ∠XMQ and ∠PMY; ∠XMP and ∠YMQ are vertically opposite angles.

3. Four pairs of angles of a linear pair are formed.

4. ∠XMQ and ∠QMY; ∠QMY and ∠YMP; ∠YMP and ∠PMX; ∠PMX and ∠XMQ are the angles forming a linear pair.

5. Given, m∠XMQ = 90°m∠XMP = m∠XMQ ….[angles of a linear pair]⇒m∠XMP + 90° = 180°⇒ m∠XMP = 90°

m∠XMP= m∠YMQ = 90° ….[Vertically Opposite angles]

⇒ m∠XMP = 180° – 90° = 90°

m∠XMP + m∠XMQ = 180°

m∠PMY = m∠XMQ = 90° ….[Vertically Opposite angles]

**Activity**

**Solution 1:**

**Solution 2:**

**Solution 3:**

(1) Measure of ∠ABC is 30°.

(2) Measure of ∠DEF is 60°.

(3) The sum of the measures of both angles in fig(a) is 90°.

(4) The sum of the measures of both angles in fig(b) is 90°.

**Solution 4:**

(1) The measure of m∠KLM is 30°.

(2) The sum of m∠KLM and m∠HIJ is 180°.

(3) Then sum of m∠WYZ and m∠WYX is 180°

**Solution 5:**

**Solution 6:**

**Practice – 1**

**Solution 1(1):**

2. 70˚

The measure of given angle = 60˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle = 90˚ – 20˚ = 70˚

∴ Measure of its complementary angle is 70˚.

**Solution 1(2):**

1. 25˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle

The measure of given angle = 55˚

∴ Measure of its complementary angle = 90˚ – 55˚ = 25˚

**Solution 1(3):**

1. 7˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle

The measure of given angle = 83˚

∴ Measure of its complementary angle = 90˚ – 83˚ = 7˚

**Solution 2:**

Calculations:

1. The measure of given angle = 50˚

∴ Measure of its complementary angle = 90˚ – 50˚ = 40˚

2. The measure of given angle = 63˚

∴ Measure of its complementary angle = 90˚ – 63˚ = 27˚

3. The measure of given angle = 47˚

∴ Measure of its complementary angle = 90˚ 47˚ = 43˚

4. The measure of given angle = 56˚

∴ Measure of its complementary angle = 90˚ – 56˚ = 34˚

5. The measure of given angle = 12˚

∴ Measure of its complementary angle = 90˚ – 12˚ = 78˚

6. The measure of given angle = 67˚

∴ Measure of its complementary angle = 90˚ – 67˚ = 23˚

**Solution 3:**

The measure of given angle = 23˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle = 90˚- 23˚ = 67˚

∴ Measure of its complementary angle is 67˚.

**Solution 4:**

The measure of given angle = 36˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle = 90˚ – 36˚ = 54˚

∴ Measure of its complementary angle is 54˚.

**Solution 5:**

- The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 15˚ + 75˚ = 90˚

Hence, the given pair of angles is a pair of complementary angles. - The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 75˚ + 47˚= 123˚ ≠ 90˚

Hence, the given pair of angles is not a pair of complementary angles. - The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 64˚ + 26˚ = 90˚

Hence, the given pair of angles is a pair of complementary angles. - The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 50˚ + 40˚ = 90˚

Hence, the given pair of angles is a pair of complementary angles. - The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 33˚ + 66˚

= 99˚ ≠ 90˚

Hence, the given pair of angles is not a pair of complementary angles. - The sum of measures of two complementary angles = 90˚. The sum of measures of given two angles = 20˚ + 70˚ = 90˚

Hence, the given pair of angles is a pair of complementary angles.

**Solution 6:**

- The measure of an acute angle = 35˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle

∴ Measure of its complementary angle = 90˚ – 35˚ = 55˚ - The measure of an acute angle = 22˚

Measure of complementary angle of an angle = 90˚ – the measure of the given angle

∴ Measure of its complementary angle = 90˚ – 22˚ = 68˚ - The measure of an acute angle = 59˚

Measure of complementary angle of an angle = 90˚ -the measure of the given angle

∴ Measure of its complementary angle = 90˚ – 59˚ = 31˚

**Practice – 2**

**Solution 1:**

- Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 47˚

∴ Measure of its complementary angle = 180˚ – 47˚ = 133˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 75˚

∴ Measure of its complementary angle = 180˚ – 75˚ = 105˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 112˚

∴ Measure of its complementary angle = 180˚ – 112˚ = 68˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 90˚

∴ Measure of its complementary angle = 180˚ – 90˚ = 90˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 109˚

∴ Measure of its complementary angle = 180˚ – 109˚ = 71˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 100˚

∴ Measure of its complementary angle = 180˚ – 100˚ = 80˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 81˚

∴ Measure of its complementary angle = 180˚ – 81˚ = 99˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 60˚

∴ Measure of its complementary angle = 180˚ – 60˚ = 120˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 145˚

∴ Measure of its complementary angle = 180˚ – 145˚ = 35˚ - Measure of supplementary angle of an angle = 180˚ – the measure of the given angle

The measure of given angle = 132˚

∴ Measure of its complementary angle = 180˚ – 132˚ = 48˚

**Solution 2:**

The sum of measures of a pair of supplementary angles = 180˚ The measure of given angle = 66˚

The measure of its supplementary angle = 180˚ – 66˚ = 114˚

**Solution 3:**

The sum of measures of a pair of supplementary angles = 180˚

Here the measures of both angles are equal

∴The measure of each given angle = 180 ÷ 2 = 90˚

The measure of each angle = 90˚

**Practice – 3**

**Solution 1:**

- Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 20˚

∴Measure of angle forming its linear pair = 180˚ – 20˚ = 160˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 130˚

∴Measure of angle forming its linear pair = 180˚ – 130˚ = 50˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 111˚

∴Measure of angle forming its linear pair = 180˚ – 111˚ = 69˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 50˚

∴Measure of angle forming its linear pair = 180˚ – 50˚ = 130˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 85˚

∴Measure of angle forming its linear pair = 180˚ – 85˚ = 95˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 107˚

∴Measure of angle forming its linear pair = 180˚ – 107˚ = 73˚ - Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The measure of given angle = 155˚

∴Measure of angle forming its linear pair = 180˚ – 155˚ = 25˚

**Solution 2:**

The measure of given angle = 82˚

Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

∴Measure of angle forming its linear pair = 180˚ – 82˚ = 98˚

**Solution 3:**

Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

The given angle is a right angle.

∴The measure of this angle = 90˚

∴Measure of angle forming its linear pair = 180˚ – 90˚ = 90˚

**Solution 4:**

Angles forming a linear pair are always supplementary.

∴The sum of measures of angles of a linear pair = 180˚

∴The measure of the given angle = 108˚

∴Measure of angle forming its linear pair = 180˚ – 108˚ = 72˚

**Solution 5:**

- 27˚ and 153˚

(27˚ + 153˚ = 180˚) - 90˚ and 90˚

(90˚ + 90˚ = 180˚) - 130˚ and 50˚

(130˚ + 50˚ = 180˚) - 80˚ and 100˚

(80˚ + 100˚ = 180˚) - 35˚ and 145˚

(35˚ + 145˚ = 180˚)

**Practice – 4**

**Solution 1:**

1. Vertically opposite angle of ∠XVZ is ∠WVY

2. Vertically opposite angle of ∠XVW is ∠YVZ

3. m∠XVW = 120˚ then,

i. m∠WVY = 60˚

Calculation:

∠XVZ and ∠WVY form a linear pair.

∴m∠XVZ + m∠WVY = 180˚

m∠XVW = 120˚

∴m∠WVY = 180˚ – 120˚ = 60˚

ii. m∠XVZ = 60˚

Calculation:

∠XVW and ∠XVZ form a linear pair.

∴m∠XVW+ m∠XVZ = 180˚

m∠XVW = 120˚

∴ m∠XVYZ = 180˚ – 120˚ = 60˚

**Solution 2:**

**Solution 3:**

The angles of linear pairs are always supplementary.

In the given figure, the two pairs of supplementary angles are:

∠EFH and ∠GFH

∠EFI and ∠GFI