An angle complementary to:
a) 50° is 40°
b) 20° is 70°
c) π/4 is π/4
d) π/6 is π/3
An angle supplementary to:
a) 50° is 130°
b) 20° is 160°
c) π/4 is 3π/4
d) π/6 is 5π/6
Two angles coterminal with an angle of 150° are -210° and 510°.
And, two angles coterminal with an angle measuring 5π/3 are (-π/3) and (11π/3).
When the sum of two angles is equal to 90 degrees, then they are Complementary to each other, or together, they are called Complementary Angles.
Here, for (a) An angle complementary to 50° is
For (b) An angle complementary to 20° is °.
For (c) An angle complementary to π/4 is , since (π/2 = 90°).
And, for (c) An angle complementary to π/3 is .
When the sum of two angles is equal to 180 degrees, then they are Supplementary to each other, or together, they are called Supplementary Angles.
Here, for (a) An angle Supplementary to 50° is °.
For (b) An angle Supplementary to 20° is °.
For (c) An angle Supplementary to π/4 is , since (π = 180°).
And, for (c) An angle Supplementary to π/3 is .
Coterminal angles are the set of angles that have the same initial side and share the terminal sides, i.e.,
Let us assume a 45° angle, lying in the first quadrant with its vertex at the origin and base side on the x-axis. Now, keeping the base side fixed on the x-axis itself, if we start rotating another ray in the clockwise direction from the x-axis around the origin, the ray will coincide with the other side of the initial 45° angle after being rotated by an angle of [-(360 - 45)° = -315°]. Hence, -315° will be a coterminal angle of 45°. Similarly, if we start rotating another ray in the anti-clockwise direction from the x-axis around the origin, the ray will coincide with the other side of the initial 45° angle after being rotated by an angle of [(360 + 45)° = 405°]. Hence, 405° will also be a coterminal angle of 45°. (Refer to the attached picture).
The formula to find the coterminal angles of any angle "θ" depending upon whether it is in terms of degrees or radians is as follows:
Degrees: (θ ± 360n)...[n = 1, 2, 3, 4, 5,...]
Radians: (θ ± 2πn)...[n = 1, 2, 3, 4, 5,...]
Therefore, Two angles coterminal with an angle of 150° are
°
and,
Similarly, Two angles coterminal with an angle measuring 5π/3 are
And, .
- Complementary Angles: When the sum of two angles is equal to 90 degrees, then they are Complementary to each other, or together, they are called Complementary Angles.
- Supplementary Angles: When the sum of two angles is equal to 180 degrees, then they are Supplementary to each other, or together, they are called Supplementary Angles.
- Coterminal angles: These are the set of angles that have the same initial side and share the terminal sides.
To learn more about Complementary Angles, click on the link below.
brainly.com/question/3027144
#SPJ4