# 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:

1. 45°

Answer: Let us assume, the required angle = x
45° + x = 180°
Or, x = 180° - 45° = 135°
Hence, the required supplementary angle = 135°
2. 25°

Answer: Let us assume, the required angle = x
25° + x = 180°
Or, x = 180° - 25° = 155°
Hence, the required supplementary angle = 155°
3. 112°

Answer: Let us assume, the required angle = x
112° + x = 180°
Or, x = 180° - 112° = 68°
Hence, the required supplementary angle = 68°
4. 130°

Answer: Let us assume, the required angle = x
130° + x = 180°
Or, x = 180° - 130° = 50°
Hence, the required supplementary angle = 50°
5. 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:

1. 35°

Answer: Let us assume, the required angle = x
35° + x = 180°
Or, x = 180° - 35° = 145°
Hence, the required supplementary angle = 145°
2. 55°

Answer: Let us assume, the required angle = x
55° + x = 180°
Or, x = 180° - 55° = 125°
Hence, the required supplementary angle = 125°
3. 110°

Answer: Let us assume, the required angle = x
110° + x = 180°
Or, x = 180° - 110° = 70°
Hence, the required supplementary angle = 70°
4. 140°

Answer: Let us assume, the required angle = x
140° + x = 180°
Or, x = 180° - 140° = 40°
Hence, the required supplementary angle = 40°
5. 75°

Answer: Let us assume, the required angle = x
75° + x = 180°
Or, x = 180° - 75° = 105°
Hence, the required supplementary angle = 105°