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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 616 · 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.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 80° (d) 50°
  2. 2.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 160° (b) 45° (c) 155° (d) 135°
  3. 3.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 120°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
  5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
  6. 6.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 135° (c) 65° (d) 160°
  7. 7.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  8. 8.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 90° (c) 35° (d) 145°
  9. 9.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
  10. 10.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 110° (c) 50° (d) 120°
  11. 11.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 60° (d) 240°
  12. 12.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
  13. 13.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 80° (d) 260°
  14. 14.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 155° (c) 110° (d) 95°
  15. 15.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 130°
  16. 16.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 70°
  17. 17.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 150°
  18. 18.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 170° (b) 50° (c) 140° (d) 10°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 140° (d) 40°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
  21. 21.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 60° (c) 120° (d) 130°
  22. 22.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 85° (d) 145°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 160° (c) 20° (d) 140°
  24. 24.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 10° (b) 90° (c) 100° (d) 170°
  25. 25.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 35° (c) 145° (d) 65°
  26. 26.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 115° (d) 100°
  27. 27.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 285° (c) 75° (d) 105°
  28. 28.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 45° (c) 135° (d) 225°
  29. 29.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
  30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 170° (c) 190° (d) 11°
  31. 31.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 125° (d) 100°
  32. 32.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 30° (c) 75° (d) 150°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 95° (c) 85° (d) 10°
  34. 34.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 125° (d) 90°
  35. 35.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 330° (c) 30° (d) 150°
  36. 36.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 60° (b) 15° (c) 135° (d) 165°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
  38. 38.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 290° (d) 145°
  39. 39.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 145° (c) 125° (d) 160°
  40. 40.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 30° (d) 150°

Answer key

  1. 40°
  2. 135°
  3. 120°
  4. 85°
  5. 30°
  6. 20°
  7. 120°
  8. 145°
  9. 90°
  10. 50°
  11. 60°
  12. 50°
  13. 100°
  14. 85°
  15. 95°
  16. 70°
  17. 75°
  18. 10°
  19. 20°
  20. 25°
  21. 60°
  22. 95°
  23. 160°
  24. 10°
  25. 145°
  26. 100°
  27. 105°
  28. 45°
  29. 80°
  30. 10°
  31. 80°
  32. 150°
  33. 95°
  34. 125°
  35. 150°
  36. 15°
  37. 15°
  38. 70°
  39. 125°
  40. 150°

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