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°