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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 333 · 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 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  2. 2.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 160° (c) 90° (d) 110°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
  4. 4.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 160° (c) 80° (d) 100°
  5. 5.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 55° (b) 165° (c) 140° (d) 15°
  6. 6.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 45° (b) 160° (c) 135° (d) 155°
  7. 7.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 140° (b) 70° (c) 150° (d) 110°
  8. 8.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 65° (d) 135°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
  10. 10.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 110° (c) 70° (d) 140°
  11. 11.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 150° (c) 145° (d) 30°
  12. 12.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 70°
  13. 13.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 150° (c) 85° (d) 95°
  14. 14.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 65° (d) 155°
  15. 15.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 120° (c) 35° (d) 95°
  16. 16.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 85° (c) 140° (d) 95°
  17. 17.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 115° (d) 145°
  18. 18.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 50° (d) 130°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 120° (d) 30°
  20. 20.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 25°
  21. 21.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) 110° (d) 70°
  22. 22.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 50° (c) 80° (d) 130°
  23. 23.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 140° (d) 100°
  24. 24.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 105° (c) 100° (d) 155°
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
  26. 26.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 50° (c) 145° (d) 130°
  27. 27.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 60°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 10° (c) 85° (d) 190°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 240° (c) 60° (d) 120°
  30. 30.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 115° (b) 125° (c) 120° (d) 65°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 125° (c) 55° (d) 250°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 150° (c) 300° (d) 30°
  33. 33.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 60° (d) 120°
  34. 34.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 60° (c) 61° (d) 240°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 145° (c) 36° (d) 35°
  36. 36.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 155° (b) 110° (c) 70° (d) 95°
  37. 37.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  38. 38.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 110° (b) 130° (c) 50° (d) 120°
  39. 39.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  40. 40.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 160° (b) 95° (c) 85° (d) 115°

Answer key

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

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