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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 27 · 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 straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 120° (c) 30° (d) 60°
  2. 2.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 30° (c) 115° (d) 95°
  3. 3.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 90° (d) 110°
  4. 4.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 85° (d) 95°
  5. 5.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 145° (d) 85°
  6. 6.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
  7. 7.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 270° (d) 90°
  8. 8.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 130° (c) 90° (d) 40°
  9. 9.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 90° (b) 140° (c) 270° (d) 130°
  10. 10.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
  11. 11.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 110° (d) 160°
  12. 12.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 130° (b) 160° (c) 70° (d) 110°
  13. 13.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 165° (c) 15° (d) 125°
  14. 14.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 120° (b) 70° (c) 170° (d) 10°
  15. 15.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 250° (c) 70° (d) 110°
  16. 16.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 130° (d) 50°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 10° (d) 11°
  18. 18.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 115° (c) 65° (d) 245°
  19. 19.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 90° (b) 135° (c) 91° (d) 270°
  20. 20.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 160° (d) 55°
  21. 21.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 125° (d) 160°
  22. 22.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 125° (b) 105° (c) 50° (d) 130°
  23. 23.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 155° (c) 95° (d) 110°
  24. 24.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 135° (b) 75° (c) 105° (d) 120°
  25. 25.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 66° (c) 65° (d) 245°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 55° (d) 35°
  27. 27.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 170° (b) 100° (c) 90° (d) 10°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 140° (d) 280°
  29. 29.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 150° (b) 75° (c) 105° (d) 135°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 125° (d) 55°
  31. 31.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 130° (d) 155°
  32. 32.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 80° (d) 110°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 310° (d) 130°
  34. 34.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 135° (d) 160°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
  36. 36.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 150° (d) 90°
  37. 37.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 105° (d) 115°
  38. 38.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 155° (c) 85° (d) 95°
  39. 39.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 135°
  40. 40.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 165° (d) 16°

Answer key

  1. 120°
  2. 30°
  3. 110°
  4. 95°
  5. 85°
  6. 40°
  7. 90°
  8. 40°
  9. 90°
  10. 150°
  11. 90°
  12. 110°
  13. 15°
  14. 10°
  15. 110°
  16. 130°
  17. 10°
  18. 65°
  19. 90°
  20. 55°
  21. 75°
  22. 50°
  23. 85°
  24. 75°
  25. 65°
  26. 70°
  27. 10°
  28. 140°
  29. 105°
  30. 55°
  31. 130°
  32. 100°
  33. 155°
  34. 65°
  35. 65°
  36. 150°
  37. 140°
  38. 95°
  39. 100°
  40. 15°

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