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.

supplementary angle example

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.

supplementary angle example

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°



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