What are Complementary angles ?
- Two Angles are Complementary when they add up to 90 degrees (a Right Angle).
- They don’t have to be next to each other, just so long as the total is 90 degrees.
- If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 90.
1) Check if 67° and 23° are complementary angles.
Sum of angles given = 67° + 23° = 90°
As sum of given two angles is equal to 90°
The two angles are complementary angles.
2) Check if 60° and 30° are complementary angles.
Sum of angles given = 60° + 30° = 90°
Sum of given two angles is equal to 90°
3) Check if 52° and 40° are complementary angles.
Sum of angles given = 52° + 40° = 92° ≠ 90°,
As sum of given two angles is not equal to 90°
Hence, the two angles are not complementary angles.
4) If measure of an angle is 46°. Find the measure of it's complementary angle.
Solution: Measure of given angle is 46°.
Let measure of it's complementary angle be 'a'.
then, 46° + a = 90°
a = 90° - 46° = 44°
a = 44°
What are Supplementary angles ?
- Two Angles are Supplementary when they add up to 180 degrees.
- If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180.
- They don’t have to be next to each other, just so long as the total is 180 degrees.
Example:
1) Check if 60° and 120° are supplementary angles.
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Sum of angles given = 60° + 120° = 180°
As sum of given two angles is equal to 180°,
2) Check if 50° and 130° are supplementary angles.
Sum of angles given = 50° + 130° = 180°
As sum of given two angles is equal to 180°,
3) Check if 152° and 40° are complementary angles.
Sum of angles given = 152° + 40° = 192° ≠ 180°,
As sum of given two angles is not equal to 180°
Hence, the two angles are not Supplementary angles.
4)What is the supplementary angle of 143° ?
Solution: Measure of given angle is 143°.
Let measure of it's Supplementary angle be 'a'.
then, 143° + a = 180°
a = 180° – 143° = 37°
a = 37°
1) Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.
Let the measure of one of the supplementary angles be a.
Measure of the other angle is 2 times a.
So, measure of the other angle is 2a.
If the sum of the measures of two angles is 180°, then the angles are supplementary.
So, a+2a=180°
Simplify.
3a=180°
a= 180 / 3 = 60°
Measure of one angle = a = 60°
Measure of other angle = 2a = 60 * 2 = 120 °.
Thus , required supplementary angles are 60° and 120 °.