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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 586 · 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 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 40° (d) 50°
  2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 80° (c) 50° (d) 100°
  4. 4.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 75° (c) 55° (d) 125°
  5. 5.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
  6. 6.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 105° (c) 30° (d) 210°
  7. 7.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 15° (d) 85°
  8. 8.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 160° (d) 50°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 80° (c) 100° (d) 160°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
  11. 11.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 95° (b) 140° (c) 125° (d) 55°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 75°
  13. 13.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 40° (c) 140° (d) 135°
  14. 14.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 110° (c) 115° (d) 135°
  15. 15.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 100° (b) 60° (c) 140° (d) 120°
  16. 16.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 25° (d) 115°
  17. 17.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 100°
  18. 18.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 270° (b) 125° (c) 90° (d) 145°
  19. 19.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 60° (c) 150° (d) 30°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  21. 21.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°
  22. 22.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 40°
  23. 23.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 160° (c) 110° (d) 90°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 40° (c) 110° (d) 70°
  25. 25.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
  26. 26.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 70° (d) 71°
  27. 27.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 135° (d) 45°
  28. 28.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 15° (c) 165° (d) 120°
  29. 29.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) 35° (d) 130°
  30. 30.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 80° (d) 125°
  31. 31.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 130°
  32. 32.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 110° (d) 115°
  33. 33.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 140°
  34. 34.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 270°
  36. 36.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°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 70° (d) 20°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 160° (d) 11°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 145° (c) 70° (d) 36°
  40. 40.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 160° (d) 340°

Answer key

  1. 130°
  2. 10°
  3. 50°
  4. 55°
  5. 100°
  6. 30°
  7. 15°
  8. 50°
  9. 80°
  10. 65°
  11. 55°
  12. 75°
  13. 40°
  14. 45°
  15. 60°
  16. 50°
  17. 100°
  18. 90°
  19. 150°
  20. 70°
  21. 55°
  22. 140°
  23. 110°
  24. 110°
  25. 110°
  26. 70°
  27. 135°
  28. 15°
  29. 25°
  30. 80°
  31. 75°
  32. 110°
  33. 100°
  34. 85°
  35. 135°
  36. 65°
  37. 80°
  38. 10°
  39. 35°
  40. 160°

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