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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 737 · 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 two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
  3. 3.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 140° (c) 250° (d) 110°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 70° (c) 145° (d) 35°
  5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 150°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 110° (c) 71° (d) 140°
  8. 8.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 135° (c) 100° (d) 125°
  9. 9.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 75° (c) 155° (d) 100°
  10. 10.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 160° (d) 140°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 75°
  12. 12.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 135° (d) 91°
  13. 13.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 60°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 30° (d) 120°
  15. 15.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 110° (c) 140° (d) 70°
  16. 16.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°
  17. 17.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 30° (d) 210°
  18. 18.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) 85° (d) 170°
  19. 19.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 65° (c) 115° (d) 245°
  20. 20.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 255° (c) 75° (d) 105°
  21. 21.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 35° (b) 80° (c) 145° (d) 135°
  22. 22.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 35° (c) 145° (d) 95°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 21° (c) 160° (d) 20°
  24. 24.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 135°
  27. 27.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 120° (b) 90° (c) 270° (d) 150°
  28. 28.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 20° (b) 160° (c) 85° (d) 115°
  29. 29.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 45° (b) 135° (c) 105° (d) 120°
  30. 30.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 260° (b) 160° (c) 80° (d) 100°
  31. 31.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
  32. 32.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 210° (b) 150° (c) 60° (d) 30°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 150° (c) 30° (d) 120°
  34. 34.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 80° (d) 110°
  35. 35.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 95° (d) 115°
  36. 36.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 55° (d) 325°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  38. 38.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 145° (d) 150°
  39. 39.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
  40. 40.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 135° (d) 65°

Answer key

  1. 110°
  2. 50°
  3. 70°
  4. 35°
  5. 30°
  6. 120°
  7. 70°
  8. 125°
  9. 75°
  10. 60°
  11. 75°
  12. 90°
  13. 60°
  14. 30°
  15. 110°
  16. 85°
  17. 150°
  18. 85°
  19. 65°
  20. 105°
  21. 35°
  22. 35°
  23. 20°
  24. 70°
  25. 20°
  26. 45°
  27. 90°
  28. 20°
  29. 45°
  30. 80°
  31. 35°
  32. 30°
  33. 150°
  34. 100°
  35. 85°
  36. 145°
  37. 35°
  38. 35°
  39. 80°
  40. 65°

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