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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 79 · 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 35° and 65°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 80°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 45° (d) 70°
  3. 3.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 115° (d) 150°
  4. 4.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 85° (c) 155° (d) 95°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
  6. 6.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 70°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 40° (c) 110° (d) 70°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
  9. 9.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 110° (c) 145° (d) 70°
  10. 10.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 150° (c) 85° (d) 115°
  11. 11.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  12. 12.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 75° (c) 125° (d) 130°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 70° (d) 40°
  14. 14.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 125° (d) 85°
  15. 15.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 55° (b) 155° (c) 125° (d) 150°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 100° (d) 160°
  17. 17.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
  18. 18.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 130° (b) 80° (c) 30° (d) 150°
  19. 19.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 55° (c) 105° (d) 125°
  20. 20.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 85° (b) 105° (c) 95° (d) 160°
  21. 21.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 40°
  22. 22.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 60° (c) 120° (d) 125°
  23. 23.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 155° (c) 25° (d) 335°
  24. 24.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 135° (c) 150° (d) 75°
  25. 25.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 35° (b) 160° (c) 165° (d) 15°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 50° (c) 100° (d) 130°
  27. 27.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 295° (d) 115°
  28. 28.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 125°
  29. 29.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 140° (d) 105°
  30. 30.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 205° (c) 26° (d) 155°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 200° (c) 20° (d) 100°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 95° (d) 170°
  33. 33.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 155° (d) 125°
  34. 34.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 150° (c) 20° (d) 50°
  35. 35.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 60° (b) 120° (c) 105° (d) 135°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 130° (c) 260° (d) 50°
  37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  38. 38.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) 265° (c) 95° (d) 85°
  39. 39.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 91° (d) 135°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 75° (c) 105° (d) 210°

Answer key

  1. 80°
  2. 35°
  3. 65°
  4. 95°
  5. 75°
  6. 70°
  7. 110°
  8. 45°
  9. 110°
  10. 85°
  11. 110°
  12. 75°
  13. 70°
  14. 95°
  15. 125°
  16. 80°
  17. 100°
  18. 30°
  19. 125°
  20. 95°
  21. 40°
  22. 120°
  23. 155°
  24. 150°
  25. 15°
  26. 50°
  27. 115°
  28. 75°
  29. 75°
  30. 25°
  31. 100°
  32. 85°
  33. 55°
  34. 20°
  35. 60°
  36. 130°
  37. 130°
  38. 85°
  39. 90°
  40. 105°

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