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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 580 · 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 angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
  2. 2.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 155° (d) 160°
  3. 3.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 35° (d) 145°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 86° (d) 85°
  5. 5.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 295° (c) 65° (d) 25°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
  7. 7.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 90° (c) 105° (d) 15°
  8. 8.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  9. 9.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 20° (d) 100°
  10. 10.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 125° (c) 80° (d) 100°
  11. 11.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 20° (b) 160° (c) 120° (d) 80°
  12. 12.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
  13. 13.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 95° (c) 30° (d) 150°
  14. 14.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 40° (c) 10° (d) 170°
  15. 15.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 225° (d) 45°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 65° (c) 50° (d) 230°
  17. 17.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 100° (d) 80°
  18. 18.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 70° (b) 95° (c) 110° (d) 155°
  19. 19.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
  20. 20.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°
  21. 21.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 155° (b) 35° (c) 10° (d) 170°
  22. 22.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 71° (d) 70°
  24. 24.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 140° (d) 65°
  25. 25.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 40° (b) 90° (c) 130° (d) 140°
  26. 26.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 135° (b) 155° (c) 70° (d) 110°
  27. 27.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 145° (c) 115° (d) 65°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 170° (c) 11° (d) 10°
  29. 29.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 95° (b) 65° (c) 150° (d) 115°
  30. 30.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 35° (d) 145°
  31. 31.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 70° (d) 100°
  32. 32.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 50° (d) 100°
  33. 33.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 120° (c) 59° (d) 61°
  35. 35.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 115° (d) 85°
  36. 36.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 155° (c) 110° (d) 25°
  37. 37.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 105° (c) 85° (d) 95°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 10° (d) 20°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 20° (d) 70°
  40. 40.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 100° (d) 80°

Answer key

  1. 35°
  2. 45°
  3. 145°
  4. 85°
  5. 115°
  6. 75°
  7. 15°
  8. 135°
  9. 20°
  10. 80°
  11. 20°
  12. 130°
  13. 30°
  14. 10°
  15. 45°
  16. 115°
  17. 80°
  18. 110°
  19. 85°
  20. 95°
  21. 10°
  22. 135°
  23. 70°
  24. 65°
  25. 140°
  26. 110°
  27. 115°
  28. 10°
  29. 65°
  30. 145°
  31. 110°
  32. 130°
  33. 120°
  34. 60°
  35. 95°
  36. 25°
  37. 85°
  38. 10°
  39. 80°
  40. 100°

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