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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 133 · 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 25° each. What is the third angle? (a) 155° (b) 65° (c) 130° (d) 25°
  2. 2.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 40° (b) 140° (c) 155° (d) 65°
  3. 3.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 155° (b) 100° (c) 125° (d) 80°
  4. 4.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 70°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 135° (d) 270°
  6. 6.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 125°
  7. 7.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 105°
  8. 8.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 10° (d) 100°
  9. 9.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 100° (d) 150°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 40° (d) 80°
  11. 11.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°
  12. 12.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 45° (c) 95° (d) 135°
  13. 13.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 320° (d) 140°
  14. 14.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 55° (d) 145°
  15. 15.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 105° (b) 115° (c) 40° (d) 140°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 115° (c) 65° (d) 230°
  17. 17.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 100° (d) 115°
  18. 18.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 150° (d) 90°
  19. 19.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 130°
  20. 20.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 25°
  21. 21.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 15° (c) 50° (d) 145°
  22. 22.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 30°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 260° (d) 130°
  24. 24.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 31° (d) 30°
  25. 25.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 110° (d) 145°
  26. 26.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 40° (d) 120°
  27. 27.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 295° (c) 65° (d) 115°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 30° (d) 75°
  29. 29.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 150° (d) 125°
  30. 30.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 160° (c) 45° (d) 155°
  31. 31.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  32. 32.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 75° (d) 60°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 110° (c) 140° (d) 70°
  35. 35.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 135°
  36. 36.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
  37. 37.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 85° (b) 125° (c) 95° (d) 150°
  38. 38.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 320° (b) 40° (c) 160° (d) 140°
  39. 39.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 45°
  40. 40.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 325° (d) 35°

Answer key

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

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