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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 175 · 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 angles of a triangle are 30° and 45°. What is the third angle? (a) 135° (b) 75° (c) 150° (d) 105°
  2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  3. 3.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 135° (b) 91° (c) 270° (d) 90°
  4. 4.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 140° (c) 95° (d) 85°
  5. 5.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 100° (d) 125°
  6. 6.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 130° (c) 160° (d) 50°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
  8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 140° (d) 50°
  9. 9.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 260° (c) 100° (d) 80°
  10. 10.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 35° (b) 65° (c) 150° (d) 145°
  11. 11.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 95° (d) 110°
  12. 12.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 100° (d) 10°
  13. 13.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 90°
  14. 14.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 80° (c) 145° (d) 100°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 55° (c) 125° (d) 70°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 90° (d) 46°
  17. 17.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°
  18. 18.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 85° (d) 95°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
  20. 20.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 15° (c) 16° (d) 195°
  21. 21.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 40° (d) 125°
  22. 22.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 65° (b) 140° (c) 115° (d) 105°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
  24. 24.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 220° (d) 40°
  25. 25.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 125° (c) 80° (d) 100°
  26. 26.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 85° (b) 135° (c) 95° (d) 140°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 40° (d) 60°
  28. 28.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 40° (c) 65° (d) 140°
  29. 29.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 100° (d) 80°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 100° (c) 40° (d) 140°
  31. 31.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  32. 32.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) 135° (d) 270°
  33. 33.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 50° (d) 40°
  34. 34.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 71° (d) 110°
  35. 35.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 20° (c) 80° (d) 10°
  36. 36.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 50° (c) 65° (d) 25°
  37. 37.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 91° (d) 90°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 30° (d) 60°
  39. 39.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 130° (d) 50°
  40. 40.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 130° (b) 110° (c) 50° (d) 120°

Answer key

  1. 105°
  2. 30°
  3. 90°
  4. 95°
  5. 100°
  6. 130°
  7. 70°
  8. 100°
  9. 80°
  10. 35°
  11. 95°
  12. 10°
  13. 60°
  14. 100°
  15. 125°
  16. 45°
  17. 40°
  18. 95°
  19. 75°
  20. 15°
  21. 140°
  22. 65°
  23. 15°
  24. 40°
  25. 80°
  26. 95°
  27. 30°
  28. 140°
  29. 80°
  30. 140°
  31. 40°
  32. 135°
  33. 130°
  34. 70°
  35. 20°
  36. 50°
  37. 90°
  38. 30°
  39. 130°
  40. 50°

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