На рисунке 83 ∠AOB = 56°, ∠COD = 25°. Найдите угол FOE.

Solution:
1. ∠AOF = ∠DOE as vertical angles. 2. ∠FOE + ∠EOD + ∠DOC = 180° as they are angles on a straight line. Therefore, ∠FOE = 180° - ∠EOD - ∠DOC 3. Since ∠EOD = ∠AOF, we can substitute ∠AOF into the equation: ∠FOE = 180° - ∠AOF - ∠DOC 4. We know that ∠AOB + ∠AOF + ∠FOE + ∠EOD + ∠DOC + ∠COB = 360° (full circle). And, ∠AOB + ∠DOC = 56° + 25° = 81° 5. ∠FOE + ∠EOD + ∠DOC = 180°, so ∠AOB + ∠AOF + ∠FOE + ∠EOD + ∠DOC + ∠COB = 360° can be simplified to ∠AOF = ∠DOE 6. ∠BOC=∠AOE as vertical angles. ∠AOB + ∠AOF + ∠FOE = ∠EOD + ∠DOC + ∠COB =180° (angles on a straigh line) 7. 2 * ∠FOE + ∠AOB + ∠COD = 180° 8. 2 * ∠FOE = 180° - (56° + 25°) = 99°. 9. ∠FOE = 99° / 2 = 49.5°
Answer: ∠FOE = 49.5°