Найдите все неизвестные углы: ∠1 = ∠2 = ∠3 = ∠4 = ∠5 = ∠6 = ∠7 = ∠8 = ∠9 = ∠10 = ∠11 = ∠12 = ∠13 = ∠14 = ∠15 = ∠16 = ∠17 = ∠18 = ∠19 = ∠20 = ∠21 = ∠22= ∠23 = ∠24 = ∠25 = ∠26 = ∠27 = ∠28 = ∠29 = ∠30 = ∠31 = ∠32=

Решение:

Рассмотрим углы в треугольниках, учитывая, что сумма углов в треугольнике равна 180°, а также свойства равнобедренных и равносторонних треугольников.

1. $$ ∠1 = 180° - 70° - 50° = 60° $$
2. $$ ∠2 = 60° $$
3. $$ ∠3 = 60° $$
4. $$ ∠4 = 180° - 90° - 70° = 20° $$
5. $$ ∠5 = 180° - 90° - 50° = 40° $$
6. $$ ∠6 = 20° $$
7. $$ ∠7 = 40° $$
8. $$ ∠8 = 180° - 20° - 40° = 120° $$
9. $$ ∠9 = (180° - 120°)/2 = 30° $$
10. $$ ∠10 = 180° - 90° - 17.5° = 72.5° $$
11. $$ ∠11 = 90° $$
12. $$ ∠12 = 40° $$
13. $$ ∠13 = 20° $$
14. $$ ∠14 = 180° - 75° - 15° = 90° $$
15. $$ ∠15 = 55° $$
16. $$ ∠16 = 180° - 90° - 55° = 35° $$
17. $$ ∠17 = 40° $$
18. $$ ∠18 = 20° $$
19. $$ ∠19 = 65° $$
20. $$ ∠20 = (180° - 115°)/2 = 32.5° $$
21. $$ ∠21 = 32.5° $$
22. $$ ∠22 = 180° - 115° - 32.5° = 32.5° $$
23. $$ ∠23 = 72.5° $$
24. $$ ∠24 = 17.5° $$
25. $$ ∠25 = 90° - 17.5° - 35° = 37.5° $$
26. $$ ∠26 = 37.5° $$
27. $$ ∠27 = 17.5° $$
28. $$ ∠28 = 17.5° $$
29. $$ ∠29 = 90° $$
30. $$ ∠30 = 65° $$
31. $$ ∠31 = 90° - 65° = 25° $$
32. $$ ∠32 = 80° $$

Ответ:

∠1 = 60°

∠2 = 60°

∠3 = 60°

∠4 = 20°

∠5 = 40°

∠6 = 20°

∠7 = 40°

∠8 = 120°

∠9 = 30°

∠10 = 72.5°

∠11 = 90°

∠12 = 40°

∠13 = 20°

∠14 = 90°

∠15 = 55°

∠16 = 35°

∠17 = 40°

∠18 = 20°

∠19 = 65°

∠20 = 32.5°

∠21 = 32.5°

∠22 = 32.5°

∠23 = 72.5°

∠24 = 17.5°

∠25 = 37.5°

∠26 = 37.5°

∠27 = 17.5°

∠28 = 17.5°

∠29 = 90°

∠30 = 65°

∠31 = 25°

∠32 = 80°