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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 809 · 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 angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
  2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
  3. 3.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
  4. 4.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  5. 5.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) 130° (d) 50°
  6. 6.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 120° (d) 160°
  7. 7.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  8. 8.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 75°
  9. 9.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 85°
  10. 10.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 115° (c) 295° (d) 25°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
  12. 12.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 85° (c) 95° (d) 155°
  13. 13.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 90° (c) 270° (d) 130°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 130° (d) 50°
  15. 15.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) 340° (c) 160° (d) 70°
  16. 16.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
  17. 17.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
  18. 18.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 75° (b) 110° (c) 105° (d) 145°
  19. 19.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 60°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 110° (d) 35°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 110° (d) 145°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
  23. 23.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 115° (c) 65° (d) 140°
  24. 24.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 50° (c) 51° (d) 130°
  26. 26.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 150° (b) 90° (c) 270° (d) 120°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 95° (c) 190° (d) 85°
  28. 28.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 20° (c) 65° (d) 160°
  29. 29.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 140° (c) 85° (d) 125°
  30. 30.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 125° (d) 55°
  31. 31.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 130° (d) 155°
  33. 33.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  34. 34.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 125°
  35. 35.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 140° (c) 145° (d) 105°
  36. 36.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 125° (d) 55°
  37. 37.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 135° (b) 45° (c) 155° (d) 160°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 80° (d) 160°
  39. 39.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 125° (c) 55° (d) 110°
  40. 40.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 155° (b) 65° (c) 25° (d) 140°

Answer key

  1. 45°
  2. 30°
  3. 140°
  4. 135°
  5. 130°
  6. 60°
  7. 100°
  8. 75°
  9. 95°
  10. 115°
  11. 80°
  12. 85°
  13. 90°
  14. 65°
  15. 160°
  16. 130°
  17. 40°
  18. 75°
  19. 120°
  20. 35°
  21. 145°
  22. 50°
  23. 115°
  24. 50°
  25. 50°
  26. 90°
  27. 95°
  28. 20°
  29. 85°
  30. 125°
  31. 60°
  32. 155°
  33. 90°
  34. 100°
  35. 105°
  36. 125°
  37. 135°
  38. 80°
  39. 55°
  40. 25°

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