Class 7 Maths

Supplementary Angles

Problems & Solutions:

Supplementary Angles: Two angles are supplementary to each other if their sum is equal to two right angles, i.e. equal to 180°.
Let us take example of following pair of angles, shown in the figure.

Since, 40° + 140° = 180°

So, these are supplementary to each other. In other words, these angles make a pair of supplementary angles.

Example: Find if the following angles make a pair of supplementary angles.

Solution: 60° + 120° = 180°

As the sum of these angles is equal to two right angles, so they make a pair of supplementary angles.

Question: Find the supplementary angles for following angles:

(a) 45°

Answer: Let us assume, the required angle = x

45° + x = 180°

Or, x = 180° - 45° = 135°

Hence, the required supplementary angle = 135°

(b) 25°

Answer: Let us assume, the required angle = x

25° + x = 180°

Or, x = 180° - 25° = 155°

Hence, the required supplementary angle = 155°

(c) 112°

Answer: Let us assume, the required angle = x

112° + x = 180°

Or, x = 180° - 112° = 68°

Hence, the required supplementary angle = 68°

(d) 130°

Answer: Let us assume, the required angle = x

130° + x = 180°

Or, x = 180° - 130° = 50°

Hence, the required supplementary angle = 50°

(e) 78°

Answer: Let us assume, the required angle = x

78° + x = 180°

Or, x = 180° - 78° = 102°

Hence, the required supplementary angle = 102°

Question: Find the supplementary angles for following angles:

(a) 35°

Answer: Let us assume, the required angle = x

35° + x = 180°

Or, x = 180° - 35° = 145°

Hence, the required supplementary angle = 145°

(b) 55°

Answer: Let us assume, the required angle = x

55° + x = 180°

Or, x = 180° - 55° = 125°

Hence, the required supplementary angle = 125°

(c) 110°

Answer: Let us assume, the required angle = x

110° + x = 180°

Or, x = 180° - 110° = 70°

Hence, the required supplementary angle = 70°

(d) 140°

Answer: Let us assume, the required angle = x

140° + x = 180°

Or, x = 180° - 140° = 40°

Hence, the required supplementary angle = 40°

(e) 75°

Answer: Let us assume, the required angle = x

75° + x = 180°

Or, x = 180° - 75° = 105°

Hence, the required supplementary angle = 105°