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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 104 · 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 two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 125° (d) 35°
  2. 2.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 105° (b) 160° (c) 75° (d) 125°
  3. 3.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 140° (d) 85°
  4. 4.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 80° (d) 125°
  5. 5.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 65° (d) 145°
  6. 6.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 270°
  7. 7.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 150° (b) 75° (c) 45° (d) 135°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 80° (c) 20° (d) 200°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 120° (d) 30°
  10. 10.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 130° (d) 80°
  11. 11.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 110°
  12. 12.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
  13. 13.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 130° (d) 65°
  15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 130° (d) 25°
  16. 16.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) 95° (c) 85° (d) 5°
  17. 17.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 115° (b) 160° (c) 65° (d) 135°
  18. 18.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (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.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 20° (c) 10° (d) 80°
  22. 22.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 75° (b) 150° (c) 105° (d) 135°
  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) 85° (b) 95° (c) 265° (d) 86°
  24. 24.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 115° (b) 100° (c) 80° (d) 145°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°
  26. 26.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 115° (c) 135° (d) 110°
  27. 27.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 85° (d) 135°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 20° (c) 40° (d) 21°
  29. 29.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 35°
  30. 30.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 280° (d) 80°
  31. 31.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 50°
  32. 32.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
  33. 33.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 285° (c) 15° (d) 75°
  34. 34.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 61° (d) 240°
  35. 35.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 115°
  36. 36.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 90° (d) 270°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 260° (c) 50° (d) 130°
  38. 38.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 15° (b) 85° (c) 110° (d) 165°
  39. 39.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 55°
  40. 40.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 260° (c) 100° (d) 80°

Answer key

  1. 70°
  2. 105°
  3. 85°
  4. 100°
  5. 65°
  6. 90°
  7. 45°
  8. 100°
  9. 60°
  10. 80°
  11. 100°
  12. 40°
  13. 90°
  14. 65°
  15. 130°
  16. 95°
  17. 115°
  18. 120°
  19. 80°
  20. 55°
  21. 20°
  22. 105°
  23. 85°
  24. 80°
  25. 155°
  26. 135°
  27. 85°
  28. 20°
  29. 145°
  30. 80°
  31. 130°
  32. 60°
  33. 105°
  34. 60°
  35. 95°
  36. 90°
  37. 130°
  38. 15°
  39. 55°
  40. 80°

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