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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 123 · 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 80° each. What is the third angle? (a) 80° (b) 10° (c) 20° (d) 100°
  2. 2.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 70° (d) 35°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
  4. 4.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 135° (c) 110° (d) 115°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 80° (d) 50°
  6. 6.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 80° (c) 100° (d) 145°
  7. 7.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 125° (b) 95° (c) 150° (d) 85°
  8. 8.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 120° (c) 160° (d) 60°
  9. 9.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 255° (c) 75° (d) 150°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 130° (c) 25° (d) 310°
  11. 11.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 30° (d) 120°
  12. 12.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 125° (b) 155° (c) 55° (d) 80°
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 40°
  14. 14.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 55° (b) 160° (c) 35° (d) 145°
  15. 15.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 160° (b) 15° (c) 165° (d) 35°
  16. 16.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 80°
  17. 17.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 100°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 70°
  19. 19.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) 340° (d) 160°
  20. 20.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 30° (d) 31°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  22. 22.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 150° (b) 100° (c) 80° (d) 110°
  23. 23.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 135° (d) 315°
  24. 24.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 35° (c) 145° (d) 70°
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 30° (c) 61° (d) 120°
  26. 26.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 115° (d) 65°
  27. 27.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 20° (d) 70°
  29. 29.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 125° (c) 25° (d) 80°
  30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 11° (c) 10° (d) 170°
  31. 31.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 160°
  33. 33.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 91° (d) 135°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 250° (d) 125°
  35. 35.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 115° (c) 145° (d) 150°
  36. 36.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
  37. 37.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 85° (c) 50° (d) 130°
  38. 38.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 155° (c) 160° (d) 135°
  39. 39.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 46° (c) 225° (d) 135°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 30° (d) 150°

Answer key

  1. 20°
  2. 70°
  3. 85°
  4. 45°
  5. 40°
  6. 100°
  7. 95°
  8. 60°
  9. 75°
  10. 155°
  11. 120°
  12. 55°
  13. 80°
  14. 35°
  15. 15°
  16. 80°
  17. 100°
  18. 60°
  19. 160°
  20. 30°
  21. 75°
  22. 80°
  23. 135°
  24. 145°
  25. 60°
  26. 50°
  27. 30°
  28. 55°
  29. 25°
  30. 10°
  31. 70°
  32. 10°
  33. 90°
  34. 125°
  35. 115°
  36. 130°
  37. 50°
  38. 135°
  39. 45°
  40. 150°

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