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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 8 · 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 60° and 50°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 70°
  2. 2.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 135° (d) 125°
  3. 3.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 10° (d) 95°
  4. 4.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 270° (c) 145° (d) 90°
  5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
  6. 6.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 50° (c) 115° (d) 130°
  7. 7.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 140° (b) 40° (c) 145° (d) 75°
  8. 8.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 145° (d) 290°
  10. 10.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 135° (d) 45°
  11. 11.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 110° (d) 90°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
  13. 13.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 95° (d) 75°
  14. 14.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 25° (c) 80° (d) 125°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 260° (d) 130°
  16. 16.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 155° (c) 105° (d) 100°
  17. 17.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 95° (b) 135° (c) 85° (d) 140°
  18. 18.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 160° (c) 20° (d) 145°
  19. 19.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) 170° (c) 190° (d) 11°
  20. 20.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) 50° (d) 140°
  21. 21.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 160° (d) 45°
  22. 22.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 66° (c) 115° (d) 65°
  23. 23.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 15° (c) 35° (d) 160°
  24. 24.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 100° (d) 30°
  25. 25.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 150° (d) 145°
  26. 26.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 110° (d) 70°
  27. 27.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  28. 28.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 135° (c) 45° (d) 90°
  29. 29.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 45°
  30. 30.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 145° (b) 125° (c) 55° (d) 160°
  31. 31.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 125° (c) 55° (d) 56°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 66° (d) 130°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 70° (d) 160°
  34. 34.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 220° (c) 140° (d) 40°
  35. 35.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 90° (c) 130° (d) 140°
  36. 36.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 140° (b) 40° (c) 160° (d) 320°
  37. 37.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 75° (c) 255° (d) 150°
  38. 38.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 75°
  39. 39.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 25° (b) 155° (c) 135° (d) 70°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°

Answer key

  1. 70°
  2. 100°
  3. 10°
  4. 90°
  5. 110°
  6. 130°
  7. 40°
  8. 50°
  9. 145°
  10. 135°
  11. 110°
  12. 20°
  13. 105°
  14. 25°
  15. 130°
  16. 75°
  17. 95°
  18. 20°
  19. 10°
  20. 70°
  21. 45°
  22. 65°
  23. 15°
  24. 150°
  25. 65°
  26. 70°
  27. 70°
  28. 45°
  29. 45°
  30. 125°
  31. 55°
  32. 65°
  33. 80°
  34. 140°
  35. 90°
  36. 140°
  37. 75°
  38. 105°
  39. 25°
  40. 10°

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