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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 850 · 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 65° and 95°. What is the third angle? (a) 115° (b) 85° (c) 20° (d) 160°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 160° (d) 140°
  4. 4.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 91° (c) 135° (d) 45°
  5. 5.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 40° (d) 110°
  6. 6.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°
  7. 7.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  8. 8.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 145° (b) 10° (c) 45° (d) 170°
  9. 9.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 240°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
  11. 11.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 85° (b) 95° (c) 150° (d) 125°
  12. 12.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 155° (b) 40° (c) 165° (d) 15°
  13. 13.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 35° (b) 165° (c) 15° (d) 160°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
  15. 15.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 300° (b) 60° (c) 120° (d) 150°
  16. 16.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 340° (d) 160°
  17. 17.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 40° (d) 80°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 150° (d) 75°
  19. 19.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 95° (b) 125° (c) 85° (d) 150°
  20. 20.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 120°
  21. 21.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 150° (c) 55° (d) 125°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 25° (d) 130°
  23. 23.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 75° (d) 145°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 130° (d) 260°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
  27. 27.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 135° (c) 75° (d) 150°
  28. 28.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°
  29. 29.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 45° (c) 135° (d) 46°
  30. 30.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 95° (d) 140°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
  32. 32.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 300° (c) 120° (d) 60°
  33. 33.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°
  34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
  35. 35.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 35° (c) 215° (d) 70°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 51° (c) 130° (d) 100°
  37. 37.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 115° (c) 140° (d) 105°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
  39. 39.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 80° (c) 140° (d) 100°
  40. 40.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 76° (d) 255°

Answer key

  1. 20°
  2. 110°
  3. 160°
  4. 90°
  5. 40°
  6. 70°
  7. 60°
  8. 10°
  9. 60°
  10. 35°
  11. 95°
  12. 15°
  13. 15°
  14. 80°
  15. 120°
  16. 160°
  17. 80°
  18. 75°
  19. 95°
  20. 120°
  21. 125°
  22. 155°
  23. 105°
  24. 130°
  25. 50°
  26. 125°
  27. 150°
  28. 120°
  29. 45°
  30. 95°
  31. 65°
  32. 60°
  33. 75°
  34. 110°
  35. 35°
  36. 50°
  37. 40°
  38. 75°
  39. 80°
  40. 75°

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