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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 905 · 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 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 100° (d) 155°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 30° (d) 40°
  3. 3.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 85° (d) 95°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
  5. 5.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 240° (c) 60° (d) 121°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 30° (d) 60°
  7. 7.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 160° (b) 115° (c) 65° (d) 135°
  8. 8.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 45° (b) 100° (c) 135° (d) 125°
  9. 9.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 260° (c) 81° (d) 100°
  10. 10.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 125° (b) 120° (c) 55° (d) 115°
  11. 11.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 125° (d) 35°
  12. 12.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 45°
  13. 13.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 30° (d) 15°
  14. 14.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 130° (c) 80° (d) 50°
  15. 15.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 110° (c) 145° (d) 105°
  16. 16.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 31° (d) 150°
  17. 17.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 280° (c) 80° (d) 100°
  18. 18.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 90° (d) 125°
  19. 19.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 86° (d) 95°
  20. 20.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 60° (c) 160° (d) 140°
  21. 21.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 35°
  22. 22.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 55° (c) 235° (d) 125°
  23. 23.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°
  24. 24.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 95° (c) 85° (d) 130°
  25. 25.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 105° (c) 55° (d) 125°
  26. 26.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 160° (b) 55° (c) 125° (d) 145°
  27. 27.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 125° (d) 120°
  28. 28.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
  29. 29.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 130° (c) 100° (d) 80°
  30. 30.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
  31. 31.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 85° (c) 125° (d) 140°
  32. 32.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  33. 33.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 200° (c) 100° (d) 20°
  34. 34.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 140° (b) 105° (c) 40° (d) 115°
  35. 35.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
  36. 36.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 90° (b) 35° (c) 145° (d) 125°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  38. 38.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 155° (b) 35° (c) 145° (d) 60°
  39. 39.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  40. 40.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 30° (d) 210°

Answer key

  1. 105°
  2. 20°
  3. 95°
  4. 55°
  5. 120°
  6. 30°
  7. 115°
  8. 45°
  9. 80°
  10. 55°
  11. 145°
  12. 45°
  13. 30°
  14. 50°
  15. 75°
  16. 30°
  17. 100°
  18. 125°
  19. 85°
  20. 120°
  21. 35°
  22. 55°
  23. 115°
  24. 95°
  25. 55°
  26. 125°
  27. 125°
  28. 110°
  29. 100°
  30. 70°
  31. 85°
  32. 130°
  33. 20°
  34. 40°
  35. 110°
  36. 35°
  37. 35°
  38. 145°
  39. 10°
  40. 150°

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