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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 224 · 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 160°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 21° (d) 200°
  2. 2.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 60°
  3. 3.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 91° (d) 135°
  4. 4.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 120° (c) 105° (d) 135°
  5. 5.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 95° (c) 85° (d) 105°
  6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 10° (d) 95°
  7. 7.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 125° (d) 145°
  8. 8.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 65° (d) 25°
  9. 9.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 255°
  10. 10.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 100° (d) 40°
  11. 11.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 145° (d) 95°
  12. 12.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 35° (d) 145°
  13. 13.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 120° (d) 145°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 95° (c) 190° (d) 10°
  15. 15.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 135° (d) 105°
  16. 16.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 85° (b) 95° (c) 160° (d) 115°
  17. 17.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 95° (c) 150° (d) 115°
  18. 18.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 220° (b) 40° (c) 140° (d) 110°
  19. 19.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 165° (c) 160° (d) 35°
  20. 20.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 95° (c) 85° (d) 135°
  21. 21.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 160° (b) 80° (c) 100° (d) 260°
  22. 22.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 130° (b) 50° (c) 145° (d) 85°
  23. 23.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 130°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 65° (d) 40°
  26. 26.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 50°
  27. 27.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 90° (d) 125°
  28. 28.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 110° (d) 80°
  29. 29.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 25° (b) 155° (c) 45° (d) 160°
  30. 30.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 30° (d) 150°
  31. 31.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 150° (c) 100° (d) 80°
  32. 32.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 125° (c) 25° (d) 155°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 155° (d) 25°
  34. 34.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 105° (d) 150°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
  36. 36.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°
  37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
  38. 38.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 25° (d) 65°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°

Answer key

  1. 20°
  2. 120°
  3. 90°
  4. 135°
  5. 85°
  6. 10°
  7. 90°
  8. 115°
  9. 105°
  10. 140°
  11. 85°
  12. 145°
  13. 60°
  14. 95°
  15. 120°
  16. 95°
  17. 150°
  18. 140°
  19. 15°
  20. 95°
  21. 80°
  22. 50°
  23. 80°
  24. 45°
  25. 65°
  26. 130°
  27. 90°
  28. 100°
  29. 25°
  30. 150°
  31. 80°
  32. 25°
  33. 155°
  34. 75°
  35. 70°
  36. 100°
  37. 40°
  38. 130°
  39. 110°
  40. 40°

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