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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 804 · 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 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 90° (d) 125°
  2. 2.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 150° (d) 70°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
  4. 4.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 35° (d) 150°
  5. 5.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 45° (c) 100° (d) 135°
  6. 6.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 95° (d) 120°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 130° (d) 260°
  8. 8.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 10° (c) 170° (d) 11°
  9. 9.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 115° (d) 140°
  10. 10.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°
  11. 11.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 40° (d) 130°
  12. 12.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 100° (d) 80°
  13. 13.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 155° (d) 105°
  14. 14.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 59° (d) 60°
  16. 16.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 145° (d) 100°
  17. 17.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 150°
  18. 18.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 40° (b) 140° (c) 220° (d) 110°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 140° (d) 40°
  20. 20.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
  21. 21.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 35° (c) 215° (d) 145°
  22. 22.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 135° (d) 45°
  23. 23.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 145° (d) 75°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
  25. 25.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 65° (c) 115° (d) 135°
  26. 26.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 50° (d) 130°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 90° (c) 135° (d) 45°
  28. 28.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 115° (b) 145° (c) 150° (d) 65°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 60° (d) 120°
  32. 32.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 125° (b) 80° (c) 100° (d) 155°
  33. 33.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 45° (d) 135°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 80° (d) 160°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
  36. 36.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 70° (d) 160°
  37. 37.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 35° (b) 155° (c) 145° (d) 60°
  38. 38.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 115° (d) 110°
  39. 39.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 115° (c) 85° (d) 160°
  40. 40.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 150° (c) 55° (d) 30°

Answer key

  1. 90°
  2. 140°
  3. 75°
  4. 145°
  5. 45°
  6. 85°
  7. 130°
  8. 10°
  9. 140°
  10. 150°
  11. 130°
  12. 80°
  13. 100°
  14. 130°
  15. 60°
  16. 80°
  17. 120°
  18. 40°
  19. 20°
  20. 45°
  21. 35°
  22. 45°
  23. 140°
  24. 85°
  25. 115°
  26. 130°
  27. 45°
  28. 115°
  29. 35°
  30. 35°
  31. 30°
  32. 100°
  33. 90°
  34. 80°
  35. 60°
  36. 70°
  37. 145°
  38. 135°
  39. 65°
  40. 30°

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