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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 230 · 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 50° and 35°. What is the third angle? (a) 95° (b) 145° (c) 85° (d) 130°
  2. 2.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 120°
  3. 3.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 110°
  4. 4.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 150° (d) 105°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
  6. 6.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 110° (d) 145°
  7. 7.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 155° (d) 115°
  8. 8.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 160° (c) 20° (d) 85°
  9. 9.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 41° (c) 140° (d) 220°
  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) 60° (b) 150° (c) 30° (d) 330°
  11. 11.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
  12. 12.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) 16° (d) 165°
  13. 13.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 320° (c) 40° (d) 50°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
  15. 15.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 120° (d) 90°
  16. 16.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 135° (d) 35°
  17. 17.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 25° (c) 120° (d) 155°
  18. 18.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 50° (d) 130°
  19. 19.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 60° (c) 240° (d) 120°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 140° (d) 70°
  21. 21.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 145° (c) 105° (d) 75°
  22. 22.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 40° (b) 70° (c) 150° (d) 140°
  23. 23.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 105° (d) 75°
  24. 24.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 5° (d) 10°
  25. 25.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 105° (d) 145°
  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 80° and 65°. What is the third angle? (a) 35° (b) 100° (c) 145° (d) 115°
  28. 28.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 105° (d) 110°
  29. 29.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
  30. 30.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 115° (d) 65°
  31. 31.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) 45° (c) 225° (d) 46°
  32. 32.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 70° (b) 135° (c) 110° (d) 155°
  33. 33.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 10° (c) 50° (d) 170°
  34. 34.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 235° (c) 55° (d) 125°
  35. 35.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 110° (d) 85°
  36. 36.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 100° (c) 125° (d) 45°
  37. 37.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 65° (d) 115°
  38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 25° (d) 15°
  40. 40.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 100° (d) 80°

Answer key

  1. 95°
  2. 85°
  3. 80°
  4. 150°
  5. 50°
  6. 110°
  7. 115°
  8. 20°
  9. 40°
  10. 150°
  11. 25°
  12. 15°
  13. 140°
  14. 135°
  15. 150°
  16. 145°
  17. 25°
  18. 130°
  19. 60°
  20. 70°
  21. 105°
  22. 40°
  23. 30°
  24. 10°
  25. 110°
  26. 85°
  27. 35°
  28. 105°
  29. 130°
  30. 115°
  31. 45°
  32. 110°
  33. 10°
  34. 55°
  35. 95°
  36. 45°
  37. 115°
  38. 80°
  39. 15°
  40. 100°

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