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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 769 · 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 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 110°
  2. 2.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 91° (c) 135° (d) 45°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
  4. 4.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 270° (d) 115°
  5. 5.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 130° (b) 60° (c) 110° (d) 120°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 80° (d) 100°
  8. 8.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 310° (c) 50° (d) 130°
  9. 9.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 75°
  10. 10.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 20° (d) 70°
  11. 11.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 50° (d) 140°
  12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 70° (d) 35°
  13. 13.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°
  14. 14.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 155° (c) 95° (d) 85°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
  16. 16.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 150°
  17. 17.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°
  18. 18.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 85° (b) 95° (c) 150° (d) 115°
  19. 19.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 245° (b) 115° (c) 130° (d) 65°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 25° (c) 26° (d) 155°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 66° (d) 65°
  22. 22.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 160° (d) 45°
  23. 23.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 300° (b) 150° (c) 60° (d) 120°
  24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 100° (d) 80°
  25. 25.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 80° (d) 260°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
  27. 27.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 55° (c) 235° (d) 110°
  28. 28.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 160° (c) 75° (d) 105°
  29. 29.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°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
  31. 31.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 150° (c) 120° (d) 90°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  33. 33.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 135° (c) 75° (d) 150°
  34. 34.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 115° (b) 155° (c) 65° (d) 140°
  35. 35.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 130° (c) 135° (d) 95°
  36. 36.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 140° (c) 85° (d) 95°
  37. 37.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 290° (c) 110° (d) 70°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 121° (d) 60°
  39. 39.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
  40. 40.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 110° (b) 160° (c) 20° (d) 90°

Answer key

  1. 105°
  2. 90°
  3. 60°
  4. 90°
  5. 60°
  6. 85°
  7. 80°
  8. 130°
  9. 75°
  10. 110°
  11. 140°
  12. 70°
  13. 145°
  14. 95°
  15. 155°
  16. 120°
  17. 20°
  18. 85°
  19. 65°
  20. 25°
  21. 65°
  22. 135°
  23. 60°
  24. 20°
  25. 80°
  26. 15°
  27. 55°
  28. 75°
  29. 85°
  30. 45°
  31. 90°
  32. 80°
  33. 150°
  34. 115°
  35. 135°
  36. 95°
  37. 70°
  38. 120°
  39. 110°
  40. 20°

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