he difference between the measures of the supplement and the complement of an angle is 90°
right or wrong
Answers
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It is true that
"The difference between Supplementary angle and Complementary angle of an angle is 90°"
Given:
The difference between the measures of the supplement and the complement of an angle is 90°
To find:
Check whether given statement is right or wrong
Solution:
Let's remember few points about the supplementary and the complementary angles
Supplementary angles:
- The pair of angles whose sum up to 180° are known as Supplementary angles
- The Supplementary angle of A is (180-A)°
- Example: (90°, 90°) (160°, 30°) etc.
Complementary angles:
- The pair of angles whose sum up to 90° are known as Complementary angles
- The Supplementary angle of A is (90-A)°
- Example: (45°, 45°) (40°, 50°) etc.
Let P be a angle
Supplementary angle of P = (180 - P)°
Complementary angle of P = (90 - P)°
Now find difference between Supplementary angle of P and Complementary angle of P
⇒ (180 - P)° - (90 - P)° = 180° - P - 90° + P = 90°
Therefor, we can conclude that
The difference between Supplementary angle and Complementary angle of an angle will be 90°
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