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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 47 · 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 30°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 150°
  2. 2.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 80° (c) 135° (d) 100°
  3. 3.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
  4. 4.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 120° (d) 105°
  5. 5.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 35° (c) 215° (d) 145°
  6. 6.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 70°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 20° (d) 80°
  8. 8.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 85° (d) 10°
  9. 9.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 115° (d) 140°
  10. 10.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
  11. 11.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 150° (c) 75° (d) 135°
  12. 12.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 35° (c) 15° (d) 160°
  13. 13.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 95° (c) 135° (d) 45°
  14. 14.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 125° (d) 270°
  15. 15.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 80° (b) 150° (c) 130° (d) 100°
  16. 16.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 130° (d) 50°
  17. 17.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 70° (c) 150° (d) 100°
  18. 18.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 40° (c) 140° (d) 105°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 145° (d) 36°
  20. 20.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 135° (d) 45°
  21. 21.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 100°
  22. 22.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 125° (d) 80°
  23. 23.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 125° (d) 55°
  24. 24.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 270° (c) 160° (d) 90°
  25. 25.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 130° (c) 50° (d) 85°
  26. 26.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
  27. 27.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 40° (d) 140°
  28. 28.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 170° (c) 40° (d) 10°
  29. 29.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 70° (b) 145° (c) 105° (d) 110°
  30. 30.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 115° (d) 65°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 200° (c) 20° (d) 100°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 55°
  33. 33.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 45°
  34. 34.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 160° (d) 85°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 65° (d) 40°
  36. 36.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 50° (d) 10°
  37. 37.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 110° (b) 120° (c) 70° (d) 130°
  38. 38.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°
  39. 39.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 165° (c) 125° (d) 15°
  40. 40.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 155° (d) 65°

Answer key

  1. 115°
  2. 100°
  3. 125°
  4. 105°
  5. 35°
  6. 110°
  7. 80°
  8. 10°
  9. 140°
  10. 105°
  11. 135°
  12. 15°
  13. 45°
  14. 90°
  15. 100°
  16. 50°
  17. 70°
  18. 40°
  19. 35°
  20. 45°
  21. 100°
  22. 100°
  23. 125°
  24. 90°
  25. 50°
  26. 85°
  27. 140°
  28. 10°
  29. 70°
  30. 115°
  31. 100°
  32. 45°
  33. 135°
  34. 85°
  35. 65°
  36. 10°
  37. 70°
  38. 25°
  39. 15°
  40. 155°

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