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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 797 · 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 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 30° (d) 150°
  2. 2.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) 25° (c) 65° (d) 115°
  3. 3.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 140° (c) 45° (d) 85°
  4. 4.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 115° (c) 85° (d) 95°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 35° (d) 110°
  6. 6.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 60° (c) 150° (d) 120°
  7. 7.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 130° (d) 95°
  8. 8.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
  10. 10.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 55° (b) 125° (c) 80° (d) 155°
  11. 11.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 125° (b) 40° (c) 95° (d) 140°
  12. 12.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 80°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 135° (c) 45° (d) 90°
  14. 14.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 40°
  15. 15.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 160° (d) 80°
  16. 16.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 10° (d) 100°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
  18. 18.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  19. 19.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 105° (b) 155° (c) 130° (d) 75°
  20. 20.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 145° (b) 100° (c) 115° (d) 65°
  21. 21.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 80° (c) 115° (d) 165°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 170°
  23. 23.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 145° (b) 110° (c) 75° (d) 105°
  24. 24.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 135° (d) 130°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 110° (d) 70°
  26. 26.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 130° (c) 80° (d) 100°
  27. 27.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 135° (d) 65°
  28. 28.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 80°
  29. 29.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 145° (c) 75° (d) 105°
  30. 30.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 120° (c) 105° (d) 135°
  31. 31.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 50° (d) 130°
  32. 32.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) 100° (d) 10°
  33. 33.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 155° (c) 100° (d) 105°
  34. 34.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 100° (b) 95° (c) 15° (d) 165°
  35. 35.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 80°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 65° (d) 66°
  37. 37.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) 86° (c) 95° (d) 85°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 145° (c) 35° (d) 70°
  39. 39.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 155° (d) 125°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 310° (c) 155° (d) 25°

Answer key

  1. 75°
  2. 115°
  3. 135°
  4. 85°
  5. 145°
  6. 120°
  7. 95°
  8. 90°
  9. 60°
  10. 55°
  11. 40°
  12. 80°
  13. 135°
  14. 140°
  15. 100°
  16. 10°
  17. 65°
  18. 130°
  19. 105°
  20. 65°
  21. 15°
  22. 10°
  23. 75°
  24. 95°
  25. 35°
  26. 80°
  27. 65°
  28. 80°
  29. 75°
  30. 45°
  31. 50°
  32. 50°
  33. 75°
  34. 15°
  35. 100°
  36. 65°
  37. 85°
  38. 35°
  39. 55°
  40. 155°

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