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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 165 · 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 30° and 55°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 85° (d) 95°
  2. 2.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 120° (d) 130°
  3. 3.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 135° (b) 130° (c) 85° (d) 95°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
  5. 5.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 170° (b) 10° (c) 110° (d) 80°
  6. 6.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°
  7. 7.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 80° (c) 140° (d) 280°
  8. 8.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 210° (c) 150° (d) 31°
  9. 9.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 195° (c) 16° (d) 165°
  10. 10.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 155° (b) 100° (c) 75° (d) 105°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 130° (d) 115°
  12. 12.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) 265° (c) 95° (d) 85°
  13. 13.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 105° (b) 210° (c) 150° (d) 30°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 140° (c) 280° (d) 40°
  15. 15.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 35° (d) 70°
  16. 16.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 110° (d) 115°
  17. 17.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 225°
  18. 18.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 90° (d) 145°
  19. 19.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 260° (d) 80°
  20. 20.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 55° (c) 235° (d) 110°
  21. 21.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 130° (d) 51°
  22. 22.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
  24. 24.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 20° (d) 40°
  25. 25.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 150° (b) 140° (c) 30° (d) 70°
  26. 26.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 120° (d) 115°
  27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 155° (d) 65°
  28. 28.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 160° (c) 135° (d) 45°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 300° (d) 150°
  30. 30.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 110° (b) 35° (c) 105° (d) 145°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
  32. 32.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 35° (c) 145° (d) 115°
  33. 33.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 80° (d) 220°
  34. 34.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 145° (b) 25° (c) 155° (d) 60°
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 115° (d) 65°
  36. 36.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 81° (c) 100° (d) 260°
  37. 37.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 115° (d) 130°
  38. 38.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 90° (b) 270° (c) 150° (d) 120°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
  40. 40.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 145° (c) 160° (d) 125°

Answer key

  1. 85°
  2. 110°
  3. 95°
  4. 65°
  5. 10°
  6. 75°
  7. 100°
  8. 30°
  9. 15°
  10. 75°
  11. 65°
  12. 85°
  13. 30°
  14. 140°
  15. 70°
  16. 135°
  17. 45°
  18. 145°
  19. 80°
  20. 55°
  21. 50°
  22. 10°
  23. 120°
  24. 40°
  25. 30°
  26. 125°
  27. 130°
  28. 135°
  29. 150°
  30. 35°
  31. 85°
  32. 35°
  33. 140°
  34. 25°
  35. 50°
  36. 80°
  37. 130°
  38. 90°
  39. 75°
  40. 125°

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