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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 228 · 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 105°. What is the exterior angle at the third corner? (a) 75° (b) 45° (c) 150° (d) 135°
  2. 2.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°
  3. 3.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 270° (d) 160°
  4. 4.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 130° (c) 145° (d) 95°
  5. 5.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) 5° (c) 95° (d) 85°
  6. 6.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 55° (d) 145°
  7. 7.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 150° (b) 155° (c) 125° (d) 55°
  8. 8.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 125° (b) 55° (c) 95° (d) 140°
  9. 9.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 110° (d) 30°
  10. 10.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
  11. 11.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 45° (b) 225° (c) 135° (d) 90°
  12. 12.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 10° (d) 20°
  13. 13.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 80° (b) 100° (c) 160° (d) 260°
  14. 14.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 140° (c) 100° (d) 280°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
  16. 16.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 155° (d) 110°
  17. 17.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) 55° (c) 305° (d) 125°
  18. 18.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 95° (d) 130°
  19. 19.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 125° (d) 105°
  20. 20.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 95° (c) 5° (d) 85°
  21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
  23. 23.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 100° (c) 125° (d) 155°
  24. 24.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 125° (d) 55°
  25. 25.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 155° (d) 100°
  26. 26.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  27. 27.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 25° (b) 100° (c) 105° (d) 155°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
  29. 29.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 150° (c) 100° (d) 30°
  30. 30.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
  31. 31.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 135° (d) 315°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 170° (d) 86°
  33. 33.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 45°
  34. 34.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°
  35. 35.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°
  36. 36.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) 295° (d) 65°
  37. 37.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 40° (d) 140°
  38. 38.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 100° (c) 130° (d) 80°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 300° (d) 120°

Answer key

  1. 135°
  2. 115°
  3. 90°
  4. 95°
  5. 95°
  6. 110°
  7. 125°
  8. 55°
  9. 150°
  10. 45°
  11. 135°
  12. 20°
  13. 80°
  14. 80°
  15. 120°
  16. 70°
  17. 125°
  18. 135°
  19. 130°
  20. 10°
  21. 40°
  22. 25°
  23. 100°
  24. 125°
  25. 105°
  26. 100°
  27. 25°
  28. 40°
  29. 30°
  30. 85°
  31. 135°
  32. 85°
  33. 45°
  34. 60°
  35. 65°
  36. 115°
  37. 140°
  38. 80°
  39. 50°
  40. 150°

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