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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 589 · 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.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
  2. 2.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 165° (d) 195°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 20° (d) 160°
  4. 4.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 115° (b) 230° (c) 130° (d) 50°
  5. 5.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 130° (c) 245° (d) 115°
  6. 6.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 120° (c) 100° (d) 140°
  7. 7.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 65° (c) 100° (d) 115°
  8. 8.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 130° (c) 125° (d) 55°
  9. 9.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 135° (b) 105° (c) 60° (d) 120°
  10. 10.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 110° (c) 155° (d) 95°
  11. 11.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) 30° (c) 210° (d) 31°
  12. 12.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 120° (b) 110° (c) 50° (d) 130°
  13. 13.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 150° (c) 30° (d) 55°
  14. 14.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 115° (b) 135° (c) 65° (d) 110°
  15. 15.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 105° (b) 115° (c) 140° (d) 75°
  16. 16.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 85° (c) 135° (d) 95°
  17. 17.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 20° (d) 140°
  19. 19.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 55° (b) 125° (c) 120° (d) 115°
  20. 20.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 115° (b) 145° (c) 100° (d) 65°
  21. 21.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 55° (b) 105° (c) 125° (d) 130°
  22. 22.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°
  23. 23.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 50° (d) 110°
  24. 24.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 15° (c) 120° (d) 75°
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
  26. 26.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 135° (d) 315°
  27. 27.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) 86° (c) 265° (d) 95°
  28. 28.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 110° (b) 70° (c) 140° (d) 250°
  29. 29.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 150° (d) 125°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
  31. 31.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 30° (d) 150°
  32. 32.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 320° (c) 140° (d) 40°
  33. 33.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 150° (d) 80°
  34. 34.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 135° (b) 140° (c) 85° (d) 45°
  35. 35.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 65° (d) 115°
  36. 36.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 270° (c) 90° (d) 130°
  37. 37.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 135° (d) 55°
  38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
  39. 39.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 130° (b) 60° (c) 120° (d) 110°
  40. 40.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 145° (d) 55°

Answer key

  1. 120°
  2. 15°
  3. 160°
  4. 50°
  5. 115°
  6. 40°
  7. 65°
  8. 55°
  9. 60°
  10. 85°
  11. 30°
  12. 50°
  13. 30°
  14. 65°
  15. 75°
  16. 95°
  17. 80°
  18. 20°
  19. 55°
  20. 65°
  21. 55°
  22. 50°
  23. 130°
  24. 15°
  25. 60°
  26. 135°
  27. 85°
  28. 70°
  29. 85°
  30. 95°
  31. 150°
  32. 140°
  33. 80°
  34. 45°
  35. 65°
  36. 90°
  37. 125°
  38. 100°
  39. 60°
  40. 110°

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