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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 319 · 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. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
  2. 2.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 170° (b) 85° (c) 105° (d) 10°
  3. 3.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 65°
  4. 4.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 160° (b) 55° (c) 20° (d) 145°
  5. 5.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 80°
  6. 6.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 115° (c) 130° (d) 65°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 40° (c) 220° (d) 70°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 20° (d) 70°
  9. 9.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 105° (c) 35° (d) 110°
  10. 10.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 135° (d) 75°
  11. 11.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
  12. 12.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 155° (c) 55° (d) 125°
  13. 13.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 150° (c) 125° (d) 55°
  14. 14.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  15. 15.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 120° (b) 165° (c) 75° (d) 15°
  16. 16.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 90° (c) 270° (d) 145°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 85° (d) 95°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 50° (c) 130° (d) 35°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 125° (d) 55°
  20. 20.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 110° (b) 85° (c) 95° (d) 155°
  21. 21.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 155° (b) 40° (c) 65° (d) 140°
  22. 22.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 65°
  23. 23.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 135° (c) 145° (d) 80°
  24. 24.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 85° (c) 130° (d) 145°
  25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 150° (c) 30° (d) 25°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 55° (d) 20°
  28. 28.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 135° (d) 100°
  29. 29.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 105° (c) 145° (d) 75°
  30. 30.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 75° (d) 255°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
  32. 32.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 105° (b) 115° (c) 75° (d) 140°
  33. 33.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 85° (b) 95° (c) 140° (d) 125°
  34. 34.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 45° (b) 155° (c) 160° (d) 20°
  35. 35.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 150° (b) 135° (c) 75° (d) 30°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 60° (d) 59°
  37. 37.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 40° (c) 140° (d) 105°
  38. 38.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 45°
  39. 39.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°
  40. 40.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 90° (c) 91° (d) 270°

Answer key

  1. 85°
  2. 10°
  3. 65°
  4. 20°
  5. 80°
  6. 115°
  7. 110°
  8. 80°
  9. 35°
  10. 75°
  11. 40°
  12. 55°
  13. 55°
  14. 80°
  15. 15°
  16. 90°
  17. 95°
  18. 25°
  19. 55°
  20. 85°
  21. 40°
  22. 115°
  23. 145°
  24. 95°
  25. 120°
  26. 15°
  27. 55°
  28. 80°
  29. 75°
  30. 105°
  31. 40°
  32. 75°
  33. 85°
  34. 20°
  35. 30°
  36. 60°
  37. 140°
  38. 45°
  39. 95°
  40. 90°

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