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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 84 · 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. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 95° (d) 85°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 80° (c) 100° (d) 200°
  3. 3.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 115° (b) 110° (c) 70° (d) 135°
  4. 4.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 290° (c) 70° (d) 110°
  5. 5.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  6. 6.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 100° (c) 80° (d) 145°
  7. 7.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 10° (d) 50°
  8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  9. 9.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 125° (c) 145° (d) 90°
  10. 10.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 70° (b) 100° (c) 110° (d) 150°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
  12. 12.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
  13. 13.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 315° (c) 136° (d) 45°
  14. 14.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 160° (d) 260°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 10°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 100° (d) 50°
  17. 17.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 160° (c) 115° (d) 135°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 15° (d) 30°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 160° (c) 81° (d) 100°
  20. 20.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) 160° (d) 10°
  21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
  23. 23.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 65° (c) 115° (d) 155°
  24. 24.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 160°
  25. 25.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 50° (d) 320°
  26. 26.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 160° (c) 270° (d) 110°
  27. 27.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 110° (d) 70°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  29. 29.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 225° (c) 45° (d) 46°
  30. 30.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 110° (d) 100°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 25° (d) 130°
  32. 32.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 120° (d) 150°
  33. 33.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 95° (b) 145° (c) 85° (d) 120°
  34. 34.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 210° (d) 30°
  35. 35.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 160° (d) 135°
  36. 36.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) 70° (d) 20°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 170° (c) 20° (d) 10°
  38. 38.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 105°
  39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  40. 40.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 125° (b) 160° (c) 75° (d) 20°

Answer key

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

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