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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 255 · 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 45°. What is the angle next to it on the same straight line? (a) 135° (b) 315° (c) 45° (d) 136°
  2. 2.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 160° (b) 65° (c) 135° (d) 45°
  3. 3.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 195° (d) 15°
  4. 4.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 60° (d) 120°
  5. 5.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 220° (c) 110° (d) 70°
  7. 7.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 70° (d) 135°
  8. 8.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 20° (c) 85° (d) 160°
  9. 9.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 85°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 50° (c) 155° (d) 26°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
  12. 12.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 150° (b) 270° (c) 120° (d) 90°
  13. 13.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 45° (c) 155° (d) 135°
  14. 14.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 155° (b) 45° (c) 160° (d) 135°
  15. 15.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 160° (d) 105°
  16. 16.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 130° (b) 95° (c) 145° (d) 85°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 230° (c) 65° (d) 115°
  19. 19.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 110° (b) 160° (c) 90° (d) 20°
  20. 20.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 130° (c) 50° (d) 80°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
  22. 22.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 155° (c) 65° (d) 25°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 55° (d) 250°
  24. 24.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  25. 25.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 110° (d) 120°
  26. 26.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 275° (d) 95°
  27. 27.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 105° (c) 75° (d) 255°
  28. 28.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 260° (c) 81° (d) 80°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
  30. 30.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 235° (c) 55° (d) 125°
  31. 31.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 40° (d) 130°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 30° (c) 16° (d) 15°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
  34. 34.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 105° (d) 75°
  35. 35.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 35° (c) 55° (d) 125°
  36. 36.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 150° (b) 30° (c) 90° (d) 120°
  37. 37.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 140° (d) 120°
  38. 38.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 35° (b) 145° (c) 115° (d) 100°
  39. 39.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 305° (c) 55° (d) 35°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 260° (d) 80°

Answer key

  1. 135°
  2. 135°
  3. 15°
  4. 120°
  5. 60°
  6. 110°
  7. 110°
  8. 20°
  9. 95°
  10. 25°
  11. 140°
  12. 90°
  13. 45°
  14. 135°
  15. 95°
  16. 95°
  17. 160°
  18. 115°
  19. 20°
  20. 50°
  21. 10°
  22. 155°
  23. 125°
  24. 100°
  25. 130°
  26. 95°
  27. 75°
  28. 80°
  29. 95°
  30. 55°
  31. 80°
  32. 15°
  33. 85°
  34. 75°
  35. 70°
  36. 30°
  37. 140°
  38. 35°
  39. 125°
  40. 130°

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