write the complementary, supplementary and conjugate angles for the following angles 45,75,215,30,60,90,180
Answers
Definitions:
Complementary angles: The angles that add up to 90°.
Supplementary angles: The angles that add up to 180°.
Conjugate angles: The angles that add up to 360°.
Questions and answers:
Let the unknown value for each question be x
1) 45°
Complementary angle: 45° + x = 90°
= x = 90° - 45°
= x = 45°
Supplementary angle: 45° + x = 180°
= x = 180° - 45°
= x = 135°
Conjugate angle: 45° + x = 360°
= x = 360° - 45°
= x = 315°
2) 75°
Complementary angle: 75° + x = 90°
= x = 90° - 75°
= x = 15°
Supplementary angle: 75° + x = 180°
= x = 180° - 75°
= x = 105°
Conjugate angle: 75° + x = 360°
= x = 360° - 75°
= x = 285°
3) 215°
Complementary angle: Not possible as the answer would come in negative and those types of angles are not possible.
Supplementary angle: Not possible as the answer would come in negative and those types of angles are not possible.
Conjugate angles: 215° - x = 360°
= x = 360° - 215°
= x = 145°
4) 30°
Complementary angle: 30° + x = 90°
= x = 90° - 30°
= x = 60°
Supplementary angle: 30° + x = 180°
= x = 180° - 30°
= x = 150°
Conjugate angle: 30° + x = 360°
= x = 360° - 30°
= x = 330°
5) 60°
Complementary angle: 60° + x = 90°
= x = 90° - 60°
= x = 30°
Supplementary angle: 60° + x = 180°
= x = 180° - 60°
= x = 120°
Conjugate angle: 60° + x = 360°
= x = 360° - 60°
= x = 300°
6) 90°
Complementary angle = Not possible as the answer would come as 0° and those types of angles are not possible.
Supplementary angle: 90° + x = 180°
= x = 180° - 90°
= x = 90°
Conjugate angle: 90° + x = 360°
= x = 360° - 90°
= x = 270°
7) 180°
Complementary angle: Not possible as the answer would come in negative and those types of angles are not possible.
Supplementary angle: Not possible as the answer would come as 0° and those types of angles are not possible.
Conjugate angle: 180° + x = 360°
= x = 360° - 180°
= x = 180°
Hope it helps you!
Solution :-
We know that,
- Complementary angles :- Two angles whose sum is equal to 90° .
- Supplementary angles :- Two angles whose sum is equal to 180° .
- Conjugate angles :- Two angles whose sum is equal to 360° .
So,
1) 45°
→ Complementary angle = 90° - 45° = 45°
→ Supplementary angle = 180° - 45° = 135°
→ Conjugate angle = 360° - 45° = 315°
2) 75°
→ Complementary angle = 90° - 75° = 15°
→ Supplementary angle = 180° - 75° = 105°
→ Conjugate angle = 360° - 75° = 285°
3) 215°
→ Conjugate angle = 360° - 215° = 145°
4) 30°
→ Complementary angle = 90° - 30° = 60°
→ Supplementary angle = 180° - 30° = 150°
→ Conjugate angle = 360° - 30° = 330°
5) 60°
→ Complementary angle = 90° - 60° = 30°
→ Supplementary angle = 180° - 45° = 150°
→ Conjugate angle = 360° - 45° = 330°
6) 90°
→ Supplementary angle = 180° - 90° = 90°
→ Conjugate angle = 360° - 90° = 270°
7) 180°
→ Conjugate angle = 360° - 180° = 180°
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