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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 262 · 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 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 250° (c) 125° (d) 55°
  3. 3.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
  4. 4.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 125° (c) 85° (d) 55°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
  6. 6.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 145° (c) 165° (d) 15°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 35° (c) 70° (d) 145°
  8. 8.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 75° (b) 130° (c) 155° (d) 105°
  9. 9.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 100° (c) 135° (d) 80°
  10. 10.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 25°
  11. 11.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°
  12. 12.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 145° (d) 80°
  13. 13.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 125° (c) 130° (d) 105°
  14. 14.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 86° (d) 95°
  15. 15.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 60° (d) 160°
  16. 16.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 45° (c) 135° (d) 130°
  17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 140° (d) 160°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  20. 20.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 160° (d) 155°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
  22. 22.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 255° (c) 75° (d) 150°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 80° (c) 140° (d) 41°
  24. 24.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 80° (c) 170° (d) 110°
  25. 25.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 56° (d) 235°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 100° (c) 160° (d) 81°
  27. 27.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 35°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 30° (d) 140°
  29. 29.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 120° (c) 140° (d) 60°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 170° (d) 85°
  31. 31.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 90° (b) 270° (c) 125° (d) 145°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 230° (c) 50° (d) 65°
  33. 33.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 50° (d) 130°
  34. 34.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 65° (c) 115° (d) 155°
  35. 35.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 105°
  36. 36.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 335° (d) 65°
  37. 37.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°
  38. 38.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 150° (c) 60° (d) 30°
  39. 39.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 125° (d) 55°
  40. 40.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 95°

Answer key

  1. 100°
  2. 125°
  3. 30°
  4. 55°
  5. 55°
  6. 15°
  7. 35°
  8. 105°
  9. 80°
  10. 25°
  11. 45°
  12. 80°
  13. 130°
  14. 85°
  15. 60°
  16. 45°
  17. 10°
  18. 160°
  19. 45°
  20. 45°
  21. 50°
  22. 105°
  23. 40°
  24. 10°
  25. 55°
  26. 80°
  27. 145°
  28. 20°
  29. 120°
  30. 85°
  31. 90°
  32. 115°
  33. 130°
  34. 115°
  35. 35°
  36. 155°
  37. 15°
  38. 150°
  39. 125°
  40. 95°

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