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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 363 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 45° (c) 110° (d) 115°
  2. 2.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 160° (c) 100° (d) 80°
  3. 3.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 100°
  4. 4.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 120° (b) 160° (c) 100° (d) 80°
  5. 5.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 300° (c) 120° (d) 60°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°
  7. 7.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 35° (c) 125° (d) 55°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
  9. 9.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 65° (c) 245° (d) 115°
  10. 10.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 340° (d) 70°
  11. 11.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 135° (c) 100° (d) 80°
  12. 12.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 20° (d) 110°
  13. 13.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 145° (c) 35° (d) 55°
  14. 14.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 90° (b) 125° (c) 270° (d) 145°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 66° (c) 65° (d) 115°
  16. 16.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 290° (c) 70° (d) 110°
  17. 17.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 55° (c) 125° (d) 130°
  18. 18.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 95° (b) 125° (c) 150° (d) 85°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
  20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  21. 21.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 105° (b) 155° (c) 130° (d) 75°
  22. 22.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 140°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 125° (c) 70° (d) 55°
  24. 24.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 115° (d) 150°
  25. 25.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 60° (d) 105°
  26. 26.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 65° (b) 115° (c) 125° (d) 120°
  27. 27.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 160° (b) 80° (c) 120° (d) 100°
  28. 28.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 105° (c) 100° (d) 155°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
  30. 30.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 60° (c) 130° (d) 120°
  31. 31.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 135° (c) 105° (d) 120°
  32. 32.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 15° (b) 95° (c) 165° (d) 100°
  33. 33.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 20° (d) 160°
  34. 34.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 190° (c) 10° (d) 11°
  35. 35.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  36. 36.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 31° (d) 30°
  37. 37.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 160° (c) 135° (d) 45°
  38. 38.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 155° (d) 25°
  39. 39.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 50°
  40. 40.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 85° (d) 95°

Answer key

  1. 45°
  2. 80°
  3. 65°
  4. 100°
  5. 120°
  6. 155°
  7. 125°
  8. 40°
  9. 65°
  10. 160°
  11. 80°
  12. 40°
  13. 145°
  14. 90°
  15. 65°
  16. 110°
  17. 125°
  18. 95°
  19. 55°
  20. 30°
  21. 105°
  22. 80°
  23. 125°
  24. 65°
  25. 120°
  26. 65°
  27. 100°
  28. 100°
  29. 110°
  30. 60°
  31. 75°
  32. 15°
  33. 20°
  34. 10°
  35. 130°
  36. 30°
  37. 45°
  38. 155°
  39. 50°
  40. 95°

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