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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 362 · 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 60°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 120° (d) 85°
  2. 2.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 55° (b) 135° (c) 100° (d) 125°
  3. 3.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 55° (c) 115° (d) 120°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  5. 5.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  6. 6.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
  7. 7.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  8. 8.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 95° (c) 45° (d) 135°
  9. 9.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 115° (b) 140° (c) 155° (d) 65°
  10. 10.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 260° (d) 160°
  11. 11.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
  13. 13.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 95° (d) 140°
  14. 14.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 70° (d) 110°
  15. 15.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 15° (c) 16° (d) 195°
  16. 16.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 155° (c) 110° (d) 135°
  17. 17.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) 65° (c) 66° (d) 245°
  18. 18.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 70° (b) 145° (c) 110° (d) 105°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 50° (d) 35°
  20. 20.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 160° (d) 105°
  21. 21.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 125° (d) 160°
  22. 22.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 90° (d) 155°
  23. 23.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 105° (d) 145°
  24. 24.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 65° (d) 25°
  25. 25.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 115° (c) 135° (d) 65°
  26. 26.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 45° (d) 150°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
  28. 28.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 130° (d) 75°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 140° (c) 70° (d) 110°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 170° (c) 20° (d) 11°
  31. 31.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 130° (b) 50° (c) 150° (d) 160°
  32. 32.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 30° (d) 60°
  33. 33.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) 75° (c) 15° (d) 105°
  34. 34.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°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
  36. 36.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 230° (d) 50°
  37. 37.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 100° (b) 230° (c) 130° (d) 50°
  38. 38.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 95° (b) 85° (c) 125° (d) 140°
  39. 39.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
  40. 40.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 35°

Answer key

  1. 95°
  2. 125°
  3. 55°
  4. 20°
  5. 40°
  6. 85°
  7. 100°
  8. 45°
  9. 115°
  10. 100°
  11. 85°
  12. 40°
  13. 125°
  14. 110°
  15. 15°
  16. 70°
  17. 65°
  18. 70°
  19. 25°
  20. 95°
  21. 55°
  22. 115°
  23. 75°
  24. 115°
  25. 115°
  26. 135°
  27. 70°
  28. 75°
  29. 70°
  30. 10°
  31. 130°
  32. 60°
  33. 105°
  34. 140°
  35. 75°
  36. 130°
  37. 50°
  38. 85°
  39. 75°
  40. 35°

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