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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 12 · 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. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 115° (c) 50° (d) 230°
  2. 2.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 35° (d) 145°
  3. 3.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 120° (b) 75° (c) 165° (d) 15°
  4. 4.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 10° (d) 95°
  5. 5.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 91°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 40° (d) 60°
  7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
  8. 8.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 140° (d) 150°
  9. 9.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 115° (b) 85° (c) 65° (d) 160°
  10. 10.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  11. 11.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 75°
  12. 12.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
  13. 13.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 170° (b) 10° (c) 155° (d) 35°
  14. 14.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 270° (b) 145° (c) 125° (d) 90°
  15. 15.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 115° (d) 150°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 80° (d) 50°
  17. 17.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 155° (d) 65°
  18. 18.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 295° (c) 115° (d) 65°
  19. 19.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
  21. 21.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 75° (c) 105° (d) 30°
  23. 23.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°
  24. 24.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 145° (d) 290°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
  26. 26.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 145° (d) 100°
  27. 27.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 90°
  28. 28.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 160° (c) 115° (d) 65°
  29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
  30. 30.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 35°
  31. 31.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 105° (c) 100° (d) 155°
  32. 32.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°
  33. 33.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 55° (d) 125°
  34. 34.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 160° (b) 95° (c) 85° (d) 105°
  35. 35.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 165° (b) 55° (c) 15° (d) 140°
  36. 36.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 65° (c) 115° (d) 110°
  37. 37.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 115°
  38. 38.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 60° (b) 155° (c) 25° (d) 145°
  39. 39.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 145° (c) 290° (d) 110°
  40. 40.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 70° (c) 130° (d) 110°

Answer key

  1. 115°
  2. 145°
  3. 15°
  4. 10°
  5. 90°
  6. 30°
  7. 130°
  8. 70°
  9. 65°
  10. 20°
  11. 75°
  12. 50°
  13. 10°
  14. 90°
  15. 65°
  16. 40°
  17. 115°
  18. 115°
  19. 125°
  20. 140°
  21. 70°
  22. 105°
  23. 70°
  24. 70°
  25. 60°
  26. 80°
  27. 30°
  28. 115°
  29. 100°
  30. 35°
  31. 75°
  32. 100°
  33. 125°
  34. 95°
  35. 15°
  36. 115°
  37. 115°
  38. 25°
  39. 110°
  40. 70°

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