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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 680 · 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 125°. What is the angle next to it on the same straight line? (a) 55° (b) 56° (c) 125° (d) 235°
  2. 2.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°
  3. 3.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 140° (d) 120°
  4. 4.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 150° (b) 120° (c) 300° (d) 60°
  5. 5.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 55° (d) 160°
  6. 6.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 275° (d) 85°
  7. 7.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 95° (c) 25° (d) 110°
  8. 8.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 125° (d) 75°
  9. 9.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 125° (b) 45° (c) 135° (d) 100°
  10. 10.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 135° (d) 145°
  11. 11.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 270° (c) 90° (d) 150°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
  13. 13.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°
  14. 14.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 100° (c) 105° (d) 155°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
  16. 16.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 110° (b) 135° (c) 70° (d) 115°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 145° (c) 290° (d) 110°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
  19. 19.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 130° (b) 150° (c) 80° (d) 100°
  20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 30° (d) 105°
  21. 21.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 330° (d) 150°
  22. 22.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 150° (b) 90° (c) 30° (d) 120°
  23. 23.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 125°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 66° (d) 130°
  25. 25.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 75° (c) 105° (d) 95°
  26. 26.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 95° (b) 105° (c) 160° (d) 20°
  27. 27.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 70° (c) 40° (d) 150°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 270° (d) 135°
  29. 29.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 160° (c) 50° (d) 20°
  30. 30.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  31. 31.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 80° (c) 105° (d) 100°
  32. 32.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
  33. 33.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 150° (d) 100°
  34. 34.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 120° (d) 30°
  35. 35.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 105° (c) 170° (d) 10°
  36. 36.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) 85° (c) 95° (d) 265°
  37. 37.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 30°
  38. 38.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 50° (d) 140°
  39. 39.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
  40. 40.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 130° (c) 145° (d) 95°

Answer key

  1. 55°
  2. 85°
  3. 100°
  4. 120°
  5. 55°
  6. 95°
  7. 25°
  8. 75°
  9. 45°
  10. 80°
  11. 90°
  12. 10°
  13. 50°
  14. 75°
  15. 35°
  16. 70°
  17. 145°
  18. 45°
  19. 100°
  20. 30°
  21. 150°
  22. 30°
  23. 85°
  24. 65°
  25. 75°
  26. 20°
  27. 40°
  28. 135°
  29. 20°
  30. 70°
  31. 80°
  32. 80°
  33. 80°
  34. 60°
  35. 10°
  36. 85°
  37. 150°
  38. 140°
  39. 20°
  40. 95°

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