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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 349 · 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 70°. What is each of the other two angles? (a) 110° (b) 145° (c) 35° (d) 290°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
  3. 3.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 150° (d) 105°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 270° (d) 135°
  5. 5.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 105° (b) 110° (c) 75° (d) 145°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 75° (c) 76° (d) 150°
  7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 65° (d) 25°
  8. 8.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 81° (c) 100° (d) 260°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
  10. 10.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 155° (b) 65° (c) 90° (d) 115°
  11. 11.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 25° (b) 155° (c) 125° (d) 80°
  12. 12.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 160° (c) 70° (d) 110°
  13. 13.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 95°
  14. 14.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 260° (c) 160° (d) 100°
  15. 15.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 150° (b) 155° (c) 55° (d) 30°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 40° (d) 50°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 50° (d) 130°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 240° (d) 60°
  19. 19.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 85° (b) 110° (c) 155° (d) 95°
  20. 20.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 55° (d) 235°
  21. 21.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 60° (d) 240°
  22. 22.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 95° (c) 85° (d) 5°
  23. 23.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
  24. 24.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 110° (d) 135°
  25. 25.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 55° (b) 145° (c) 125° (d) 160°
  26. 26.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) 40° (d) 65°
  27. 27.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 135° (d) 110°
  28. 28.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°
  29. 29.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 70°
  30. 30.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 40° (d) 120°
  31. 31.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 150° (c) 135° (d) 45°
  32. 32.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 80°
  33. 33.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 140° (c) 45° (d) 135°
  34. 34.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 25°
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
  36. 36.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 70° (b) 150° (c) 30° (d) 140°
  37. 37.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 95° (d) 85°
  38. 38.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 60° (b) 100° (c) 120° (d) 140°
  39. 39.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 15° (d) 75°
  40. 40.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°

Answer key

  1. 145°
  2. 25°
  3. 75°
  4. 135°
  5. 75°
  6. 75°
  7. 130°
  8. 80°
  9. 45°
  10. 65°
  11. 25°
  12. 70°
  13. 95°
  14. 100°
  15. 30°
  16. 40°
  17. 130°
  18. 120°
  19. 95°
  20. 55°
  21. 60°
  22. 95°
  23. 110°
  24. 135°
  25. 55°
  26. 65°
  27. 135°
  28. 95°
  29. 70°
  30. 140°
  31. 45°
  32. 80°
  33. 45°
  34. 25°
  35. 50°
  36. 30°
  37. 85°
  38. 60°
  39. 30°
  40. 75°

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