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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 103 · 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 110°. What is the third angle? (a) 165° (b) 70° (c) 125° (d) 15°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 140° (d) 20°
  3. 3.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) 170° (c) 11° (d) 10°
  4. 4.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) 130° (c) 40° (d) 50°
  5. 5.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 105° (b) 50° (c) 130° (d) 125°
  6. 6.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 40°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 130° (d) 50°
  8. 8.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
  10. 10.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 65° (d) 115°
  11. 11.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 65° (b) 135° (c) 115° (d) 110°
  12. 12.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 130° (c) 50° (d) 155°
  13. 13.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 135° (d) 45°
  14. 14.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 60° (b) 140° (c) 120° (d) 160°
  15. 15.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 85° (d) 95°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 120° (c) 70° (d) 30°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
  18. 18.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 95°
  19. 19.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 95° (b) 115° (c) 85° (d) 160°
  20. 20.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 155° (d) 80°
  21. 21.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 70° (c) 130° (d) 110°
  22. 22.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 85° (c) 95° (d) 140°
  23. 23.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 90° (b) 125° (c) 145° (d) 270°
  24. 24.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 35° (d) 55°
  25. 25.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 105° (d) 15°
  26. 26.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 55° (c) 25° (d) 150°
  27. 27.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 55°
  28. 28.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 160° (c) 21° (d) 20°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 20° (c) 200° (d) 80°
  30. 30.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 125° (b) 105° (c) 130° (d) 75°
  31. 31.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 75° (c) 95° (d) 105°
  32. 32.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 15° (c) 165° (d) 145°
  33. 33.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 95° (c) 30° (d) 115°
  34. 34.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 45° (c) 155° (d) 160°
  35. 35.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 70° (b) 250° (c) 140° (d) 110°
  36. 36.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 85° (d) 145°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 250° (c) 55° (d) 70°
  38. 38.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 35°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 20° (d) 170°
  40. 40.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 255° (c) 75° (d) 150°

Answer key

  1. 15°
  2. 20°
  3. 10°
  4. 130°
  5. 50°
  6. 40°
  7. 50°
  8. 140°
  9. 60°
  10. 115°
  11. 65°
  12. 50°
  13. 90°
  14. 120°
  15. 95°
  16. 60°
  17. 65°
  18. 95°
  19. 95°
  20. 80°
  21. 110°
  22. 85°
  23. 90°
  24. 125°
  25. 30°
  26. 25°
  27. 55°
  28. 20°
  29. 100°
  30. 75°
  31. 75°
  32. 15°
  33. 30°
  34. 135°
  35. 70°
  36. 130°
  37. 125°
  38. 35°
  39. 10°
  40. 75°

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