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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 135 · 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 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
  2. 2.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 75° (b) 115° (c) 140° (d) 105°
  3. 3.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 100° (c) 120° (d) 140°
  4. 4.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 45°
  5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 50° (d) 80°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 150° (c) 30° (d) 300°
  8. 8.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 200° (c) 20° (d) 100°
  9. 9.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) 110° (c) 70° (d) 71°
  10. 10.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 60° (b) 135° (c) 120° (d) 105°
  11. 11.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 95° (b) 140° (c) 125° (d) 85°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 10° (d) 80°
  13. 13.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) 55° (d) 110°
  14. 14.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 130° (b) 70° (c) 110° (d) 120°
  15. 15.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 100° (d) 35°
  16. 16.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 115° (b) 245° (c) 130° (d) 65°
  17. 17.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 70° (c) 110° (d) 155°
  18. 18.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°
  19. 19.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 70° (d) 110°
  20. 20.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 200° (d) 160°
  21. 21.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 255° (c) 75° (d) 105°
  22. 22.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 100° (d) 80°
  23. 23.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 165° (d) 195°
  24. 24.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 45° (c) 155° (d) 135°
  25. 25.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 45° (b) 10° (c) 170° (d) 145°
  26. 26.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 60° (c) 120° (d) 155°
  27. 27.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
  28. 28.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 125° (b) 150° (c) 95° (d) 85°
  29. 29.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 115° (d) 140°
  30. 30.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 65° (c) 25° (d) 335°
  31. 31.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 145° (b) 95° (c) 120° (d) 85°
  32. 32.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 135° (c) 65° (d) 160°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 40° (d) 20°
  34. 34.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
  35. 35.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 190° (c) 11° (d) 170°
  36. 36.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 150° (c) 135° (d) 75°
  37. 37.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 145° (b) 65° (c) 35° (d) 150°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 61° (c) 60° (d) 120°
  39. 39.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 145° (d) 35°
  40. 40.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 135° (d) 55°

Answer key

  1. 120°
  2. 75°
  3. 40°
  4. 135°
  5. 10°
  6. 40°
  7. 150°
  8. 20°
  9. 70°
  10. 120°
  11. 85°
  12. 50°
  13. 55°
  14. 70°
  15. 145°
  16. 65°
  17. 110°
  18. 85°
  19. 110°
  20. 20°
  21. 75°
  22. 80°
  23. 15°
  24. 45°
  25. 10°
  26. 120°
  27. 115°
  28. 95°
  29. 65°
  30. 155°
  31. 85°
  32. 20°
  33. 20°
  34. 125°
  35. 10°
  36. 135°
  37. 35°
  38. 60°
  39. 110°
  40. 125°

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