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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 274 · 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 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  2. 2.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 70°
  3. 3.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  4. 4.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
  5. 5.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 65° (b) 130° (c) 15° (d) 165°
  6. 6.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
  7. 7.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 245° (b) 115° (c) 65° (d) 130°
  8. 8.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 75°
  9. 9.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 70° (c) 130° (d) 110°
  10. 10.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 75° (b) 55° (c) 125° (d) 160°
  11. 11.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 110° (d) 55°
  13. 13.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 130° (c) 155° (d) 50°
  14. 14.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 160° (c) 115° (d) 95°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 280° (c) 40° (d) 100°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
  17. 17.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 155° (d) 55°
  18. 18.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 110° (b) 70° (c) 160° (d) 130°
  19. 19.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 85° (c) 130° (d) 95°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 40° (c) 120° (d) 60°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 70°
  22. 22.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 105° (b) 45° (c) 135° (d) 120°
  23. 23.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 90° (d) 65°
  24. 24.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 35° (c) 15° (d) 160°
  25. 25.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 55°
  26. 26.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 125° (c) 100° (d) 45°
  27. 27.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 155° (d) 45°
  28. 28.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 160° (d) 200°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 125° (c) 110° (d) 55°
  30. 30.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 115° (c) 45° (d) 110°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 46°
  32. 32.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 85° (b) 20° (c) 160° (d) 115°
  33. 33.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 115° (d) 125°
  34. 34.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 95° (c) 160° (d) 85°
  35. 35.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 305° (c) 125° (d) 35°
  36. 36.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 100° (c) 105° (d) 155°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 35° (c) 145° (d) 70°
  38. 38.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 95° (c) 115° (d) 30°
  39. 39.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) 30° (c) 31° (d) 210°
  40. 40.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 230° (c) 50° (d) 130°

Answer key

  1. 90°
  2. 70°
  3. 100°
  4. 20°
  5. 15°
  6. 40°
  7. 65°
  8. 75°
  9. 110°
  10. 55°
  11. 80°
  12. 55°
  13. 50°
  14. 95°
  15. 140°
  16. 15°
  17. 55°
  18. 110°
  19. 95°
  20. 30°
  21. 60°
  22. 45°
  23. 115°
  24. 15°
  25. 125°
  26. 45°
  27. 45°
  28. 20°
  29. 55°
  30. 45°
  31. 45°
  32. 20°
  33. 120°
  34. 85°
  35. 125°
  36. 105°
  37. 35°
  38. 30°
  39. 30°
  40. 130°

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