Angle AOB is deployed, and OC is a beam. Find the degree measures of the angles AOC and COB

Angle AOB is deployed, and OC is a beam. Find the degree measures of the angles AOC and COB if: a) the degree measure of the angle AOC is three times greater than the degree measure of the angle AOC b) the degree measure of the angle AOC is 60 (degrees) greater than the degree measure of the angle OOC c ) the degree measure of the AOC angle is 4 times less than the degree measure of the COB angle

Given:
∠АОВ – expanded;
OС-beam;
a) ∠AOC = 3∠СОВ;
b) ∠AOS-∠СОВ = 60 °;
c) ∠AOC = ∠СОВ / 4;
∠AOC =?
∠СOВ =?
Solution:
The degree measure of the unfolded angle is 180 °, which means ∠AOB = 180 °.
∠AOС + ∠СОВ = ∠АОВ;
a) ∠AOC = 3∠СОВ;
3∠СОВ + ∠СОВ = ∠АОВ;
4∠СОВ = ∠АОВ;
∠СОВ = ∠АОВ / 4;
∠СОВ = 180 ° / 4;
∠СОВ = 45 °;
∠AOС = 3∠СOВ = 3 * 45 = 135 °.
b) ∠AOС-∠СОВ = 60 °;
∠AOС-∠СОВ = 60 °;
∠АС = 60 ° + ∠СОВ;
60 ° + ∠СОВ + ∠СОВ = ∠АОВ;
2∠СОВ = ∠АОВ-60 °;
∠СОВ = (∠АОВ-60 °): 2;
∠СОВ = (180 ° -60 °): 2;
∠СОВ = 60 °.
∠АС = 60 ° + ∠СОВ = 60 ° + 60 ° = 120 °;
c) ∠AOC = ∠СОВ / 4;
∠СОВ / 4 + ∠СОВ = ∠АОВ;
5∠СОВ / 4 = ∠АОВ;
∠СОВ = 4∠АОВ / 5;
∠СOВ = 4 * 180 ° / 5 = 144 °;
∠АС = ∠СОВ / 4 = 144 ° / 4 = 36 °;
Answer: a) ∠AOC = 135 °; ∠СОВ = 45 °; b) ∠AOC = 120 °; ∠СОВ = 60 °; c) ∠AOC = 36 °; ∠СОВ = 144 °