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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 448 · 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.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 10° (d) 100°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 60° (c) 31° (d) 30°
  3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
  4. 4.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 10° (d) 85°
  5. 5.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 50° (c) 120° (d) 110°
  6. 6.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 135° (c) 150° (d) 105°
  7. 7.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 110° (c) 155° (d) 95°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 80° (d) 130°
  9. 9.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 45°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
  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) 95° (b) 265° (c) 85° (d) 86°
  12. 12.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 85° (c) 145° (d) 95°
  13. 13.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 115° (b) 135° (c) 65° (d) 110°
  14. 14.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 55° (d) 125°
  15. 15.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 85° (c) 115° (d) 160°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 10° (c) 190° (d) 85°
  17. 17.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 200° (c) 21° (d) 20°
  18. 18.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 160° (d) 110°
  19. 19.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 50° (c) 165° (d) 15°
  20. 20.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 85° (d) 160°
  21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
  22. 22.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 75° (b) 125° (c) 105° (d) 160°
  23. 23.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 35° (c) 145° (d) 215°
  24. 24.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 60°
  25. 25.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 95° (b) 130° (c) 135° (d) 50°
  26. 26.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 110° (d) 235°
  27. 27.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 80° (b) 100° (c) 260° (d) 160°
  28. 28.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 85° (b) 125° (c) 150° (d) 30°
  29. 29.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 85° (c) 155° (d) 25°
  30. 30.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 280° (b) 140° (c) 80° (d) 100°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 320° (d) 20°
  32. 32.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 140° (b) 105° (c) 65° (d) 115°
  33. 33.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 65° (b) 160° (c) 135° (d) 45°
  34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  35. 35.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 15° (b) 165° (c) 85° (d) 110°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 60° (c) 120° (d) 240°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
  38. 38.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 80° (d) 135°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
  40. 40.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 115° (c) 155° (d) 65°

Answer key

  1. 50°
  2. 30°
  3. 50°
  4. 10°
  5. 50°
  6. 105°
  7. 85°
  8. 130°
  9. 45°
  10. 80°
  11. 85°
  12. 85°
  13. 65°
  14. 125°
  15. 65°
  16. 95°
  17. 20°
  18. 90°
  19. 15°
  20. 95°
  21. 100°
  22. 105°
  23. 35°
  24. 120°
  25. 50°
  26. 125°
  27. 80°
  28. 30°
  29. 25°
  30. 100°
  31. 160°
  32. 65°
  33. 45°
  34. 110°
  35. 15°
  36. 120°
  37. 100°
  38. 80°
  39. 150°
  40. 115°

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