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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 74 · 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 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 95° (d) 85°
  2. 2.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 150° (c) 145° (d) 115°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 100° (d) 81°
  4. 4.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 140° (b) 115° (c) 65° (d) 155°
  5. 5.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 250° (c) 70° (d) 125°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 51° (d) 100°
  7. 7.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 95° (c) 105° (d) 85°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
  9. 9.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 85° (d) 95°
  10. 10.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°
  11. 11.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) 30° (d) 210°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 56° (c) 110° (d) 55°
  13. 13.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 60° (d) 150°
  14. 14.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 105° (d) 145°
  15. 15.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 280° (c) 10° (d) 80°
  16. 16.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) 76° (c) 75° (d) 105°
  17. 17.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
  18. 18.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 140° (d) 110°
  19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 130° (d) 80°
  20. 20.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 140° (d) 75°
  21. 21.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 55° (b) 110° (c) 125° (d) 235°
  22. 22.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 145° (d) 110°
  23. 23.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 135° (c) 90° (d) 45°
  24. 24.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 90° (d) 135°
  25. 25.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 41° (c) 40° (d) 220°
  26. 26.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 120° (d) 140°
  27. 27.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) 215° (c) 35° (d) 145°
  28. 28.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 80°
  29. 29.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 70° (d) 140°
  30. 30.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 60° (c) 240° (d) 120°
  31. 31.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 215° (d) 35°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 60° (d) 121°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
  35. 35.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 95° (d) 110°
  36. 36.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 80° (c) 110° (d) 150°
  37. 37.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 160° (b) 90° (c) 270° (d) 110°
  38. 38.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 105° (d) 145°
  39. 39.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 95° (d) 10°

Answer key

  1. 95°
  2. 115°
  3. 80°
  4. 115°
  5. 70°
  6. 50°
  7. 85°
  8. 45°
  9. 95°
  10. 80°
  11. 30°
  12. 55°
  13. 120°
  14. 105°
  15. 100°
  16. 75°
  17. 20°
  18. 110°
  19. 80°
  20. 75°
  21. 55°
  22. 110°
  23. 45°
  24. 90°
  25. 40°
  26. 120°
  27. 35°
  28. 80°
  29. 70°
  30. 60°
  31. 145°
  32. 120°
  33. 20°
  34. 70°
  35. 95°
  36. 80°
  37. 90°
  38. 75°
  39. 85°
  40. 95°

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