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:

  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°


Copyright © excellup 2014