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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 839 · 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 straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 105° (c) 76° (d) 75°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 160° (c) 20° (d) 40°
  4. 4.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 55° (b) 125° (c) 95° (d) 140°
  5. 5.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 135° (d) 115°
  6. 6.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 75°
  7. 7.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 10° (b) 100° (c) 90° (d) 170°
  8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
  9. 9.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 155° (c) 110° (d) 95°
  10. 10.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 125° (d) 120°
  11. 11.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 165° (d) 15°
  12. 12.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 95° (d) 5°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 160° (c) 320° (d) 140°
  14. 14.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 135° (b) 45° (c) 120° (d) 105°
  15. 15.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 300° (d) 120°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 20° (d) 80°
  18. 18.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 145° (b) 150° (c) 30° (d) 65°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
  20. 20.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 70°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 80° (c) 260° (d) 50°
  22. 22.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 95° (d) 85°
  23. 23.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 40° (d) 140°
  24. 24.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
  25. 25.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 115° (b) 270° (c) 90° (d) 155°
  26. 26.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 105°
  27. 27.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 45° (d) 135°
  28. 28.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 75° (c) 150° (d) 135°
  29. 29.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 125° (d) 145°
  30. 30.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
  31. 31.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 115° (d) 65°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
  33. 33.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 60° (d) 130°
  34. 34.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 20° (c) 290° (d) 110°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
  36. 36.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 55° (c) 150° (d) 125°
  37. 37.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 120° (c) 50° (d) 110°
  38. 38.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 105° (d) 75°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 100° (d) 80°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 20° (d) 10°

Answer key

  1. 75°
  2. 35°
  3. 20°
  4. 55°
  5. 65°
  6. 75°
  7. 10°
  8. 110°
  9. 85°
  10. 120°
  11. 15°
  12. 10°
  13. 160°
  14. 45°
  15. 120°
  16. 55°
  17. 80°
  18. 30°
  19. 65°
  20. 70°
  21. 130°
  22. 95°
  23. 100°
  24. 130°
  25. 90°
  26. 110°
  27. 135°
  28. 135°
  29. 55°
  30. 70°
  31. 50°
  32. 85°
  33. 120°
  34. 110°
  35. 75°
  36. 125°
  37. 50°
  38. 30°
  39. 100°
  40. 10°

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