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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 512 · 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 70° and 20°. What is the third angle? (a) 110° (b) 270° (c) 160° (d) 90°
  2. 2.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 60° (c) 155° (d) 145°
  3. 3.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 140° (c) 80° (d) 280°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 61° (d) 60°
  5. 5.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 160° (b) 60° (c) 140° (d) 120°
  6. 6.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 16° (c) 165° (d) 15°
  7. 7.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 160° (c) 110° (d) 20°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
  9. 9.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 40° (c) 115° (d) 140°
  10. 10.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 75° (c) 105° (d) 15°
  11. 11.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 250° (c) 70° (d) 125°
  12. 12.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 250° (b) 125° (c) 110° (d) 70°
  13. 13.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 95° (b) 145° (c) 85° (d) 120°
  14. 14.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 145° (b) 35° (c) 150° (d) 65°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 125° (c) 250° (d) 55°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 46° (c) 45° (d) 90°
  17. 17.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 65° (d) 135°
  18. 18.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
  19. 19.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 100° (d) 280°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 30° (d) 150°
  21. 21.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 160° (b) 100° (c) 260° (d) 80°
  22. 22.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 150° (b) 100° (c) 80° (d) 130°
  23. 23.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 80° (d) 41°
  25. 25.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) 100° (d) 50°
  26. 26.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) 20° (d) 30°
  27. 27.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 110° (b) 155° (c) 70° (d) 135°
  28. 28.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 30° (d) 55°
  29. 29.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 45°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  31. 31.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 120° (d) 145°
  32. 32.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 35° (c) 145° (d) 75°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 290° (c) 110° (d) 35°
  34. 34.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 25° (c) 55° (d) 150°
  35. 35.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 155° (d) 75°
  36. 36.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 160° (b) 85° (c) 115° (d) 20°
  37. 37.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 85° (d) 30°
  38. 38.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 160° (b) 100° (c) 80° (d) 120°
  39. 39.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 140° (b) 160° (c) 40° (d) 320°
  40. 40.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 170° (b) 10° (c) 110° (d) 80°

Answer key

  1. 90°
  2. 120°
  3. 100°
  4. 60°
  5. 120°
  6. 15°
  7. 20°
  8. 35°
  9. 140°
  10. 105°
  11. 110°
  12. 70°
  13. 85°
  14. 35°
  15. 125°
  16. 45°
  17. 65°
  18. 10°
  19. 100°
  20. 30°
  21. 80°
  22. 100°
  23. 130°
  24. 40°
  25. 50°
  26. 20°
  27. 110°
  28. 150°
  29. 135°
  30. 40°
  31. 60°
  32. 145°
  33. 145°
  34. 25°
  35. 75°
  36. 20°
  37. 150°
  38. 100°
  39. 140°
  40. 10°

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