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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 141 · 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 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 55° (d) 125°
  2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
  3. 3.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
  4. 4.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 95° (d) 85°
  5. 5.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 160° (c) 145° (d) 55°
  6. 6.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 125° (d) 55°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 160°
  8. 8.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 105° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 145° (d) 35°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°
  11. 11.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 270° (d) 160°
  12. 12.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°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 70° (d) 71°
  14. 14.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 55° (d) 125°
  15. 15.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 145° (d) 35°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 81° (d) 80°
  17. 17.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 80° (b) 100° (c) 120° (d) 140°
  18. 18.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 15° (b) 130° (c) 65° (d) 165°
  19. 19.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 125° (b) 115° (c) 60° (d) 120°
  20. 20.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 40°
  21. 21.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 85° (c) 95° (d) 105°
  22. 22.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 80° (d) 260°
  23. 23.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) 86° (d) 85°
  24. 24.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 40° (c) 155° (d) 140°
  25. 25.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 125° (c) 55° (d) 90°
  26. 26.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) 115° (c) 295° (d) 65°
  27. 27.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 130°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
  29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 50° (d) 65°
  30. 30.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 100° (c) 115° (d) 80°
  31. 31.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 31° (d) 30°
  32. 32.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 120° (d) 160°
  33. 33.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 130° (c) 145° (d) 50°
  34. 34.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 75° (c) 170° (d) 10°
  35. 35.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 55° (b) 155° (c) 30° (d) 150°
  36. 36.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 85° (b) 95° (c) 125° (d) 150°
  37. 37.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 120° (d) 90°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
  39. 39.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 35° (d) 145°
  40. 40.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 60° (d) 155°

Answer key

  1. 125°
  2. 30°
  3. 80°
  4. 95°
  5. 125°
  6. 125°
  7. 10°
  8. 140°
  9. 110°
  10. 40°
  11. 90°
  12. 155°
  13. 70°
  14. 70°
  15. 145°
  16. 80°
  17. 80°
  18. 15°
  19. 60°
  20. 40°
  21. 85°
  22. 80°
  23. 85°
  24. 140°
  25. 55°
  26. 115°
  27. 75°
  28. 15°
  29. 50°
  30. 80°
  31. 30°
  32. 80°
  33. 130°
  34. 10°
  35. 30°
  36. 95°
  37. 120°
  38. 80°
  39. 145°
  40. 60°

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