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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 365 · 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 40°. What is the third angle? (a) 140° (b) 105° (c) 75° (d) 145°
  2. 2.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 50° (d) 155°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
  5. 5.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 125° (b) 105° (c) 75° (d) 130°
  6. 6.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 130°
  7. 7.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 85° (b) 95° (c) 160° (d) 105°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
  9. 9.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 130° (d) 155°
  10. 10.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 100° (d) 45°
  11. 11.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 200° (d) 160°
  12. 12.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 75°
  13. 13.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) 70° (d) 20°
  14. 14.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 130° (b) 160° (c) 50° (d) 150°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 10° (c) 20° (d) 11°
  16. 16.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 120° (d) 140°
  17. 17.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 100° (b) 30° (c) 150° (d) 110°
  18. 18.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) 325° (d) 55°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 35° (d) 25°
  20. 20.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 95°
  21. 21.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 230° (d) 51°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 45° (d) 46°
  23. 23.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 145° (d) 35°
  24. 24.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 100° (d) 80°
  25. 25.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 110° (b) 50° (c) 120° (d) 130°
  26. 26.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 25° (c) 205° (d) 155°
  27. 27.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 65°
  28. 28.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 20° (d) 40°
  29. 29.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 40° (c) 140° (d) 135°
  30. 30.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 260° (d) 80°
  31. 31.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 61° (b) 120° (c) 240° (d) 60°
  32. 32.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 65° (d) 145°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
  34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  35. 35.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 125° (b) 160° (c) 55° (d) 75°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
  37. 37.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 55° (c) 115° (d) 125°
  38. 38.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 45° (d) 135°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 30° (d) 40°
  40. 40.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 90° (c) 160° (d) 270°

Answer key

  1. 105°
  2. 130°
  3. 25°
  4. 50°
  5. 75°
  6. 85°
  7. 85°
  8. 70°
  9. 130°
  10. 135°
  11. 20°
  12. 75°
  13. 80°
  14. 130°
  15. 10°
  16. 140°
  17. 30°
  18. 145°
  19. 25°
  20. 95°
  21. 50°
  22. 45°
  23. 110°
  24. 100°
  25. 50°
  26. 25°
  27. 115°
  28. 40°
  29. 40°
  30. 80°
  31. 60°
  32. 150°
  33. 65°
  34. 120°
  35. 125°
  36. 85°
  37. 55°
  38. 135°
  39. 20°
  40. 90°

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