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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 35 · 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 straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 330° (d) 30°
  2. 2.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 135° (d) 45°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 30° (d) 150°
  4. 4.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 125° (c) 105° (d) 75°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 170° (d) 20°
  6. 6.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 120° (b) 135° (c) 60° (d) 105°
  7. 7.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 40° (d) 140°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 81° (c) 80° (d) 160°
  9. 9.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 65° (d) 35°
  10. 10.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 115° (c) 150° (d) 65°
  11. 11.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 115° (b) 160° (c) 85° (d) 95°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°
  13. 13.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
  14. 14.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 90° (c) 130° (d) 270°
  15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 115° (d) 65°
  16. 16.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) 315° (c) 136° (d) 135°
  17. 17.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 45° (c) 105° (d) 135°
  18. 18.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 130° (d) 85°
  19. 19.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 150° (c) 55° (d) 155°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 55° (d) 125°
  21. 21.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 100° (c) 80° (d) 135°
  22. 22.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 35° (c) 100° (d) 145°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
  24. 24.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 130° (c) 95° (d) 145°
  25. 25.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 130° (b) 270° (c) 140° (d) 90°
  26. 26.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 150° (b) 100° (c) 80° (d) 110°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 65° (c) 66° (d) 130°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
  29. 29.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 95° (b) 75° (c) 160° (d) 105°
  30. 30.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 140° (d) 130°
  31. 31.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 140° (d) 120°
  32. 32.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 80°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
  34. 34.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 120° (c) 155° (d) 95°
  35. 35.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 70° (b) 125° (c) 250° (d) 110°
  36. 36.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 110° (c) 140° (d) 70°
  37. 37.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 150° (c) 155° (d) 55°
  38. 38.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 80°
  39. 39.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 36° (c) 70° (d) 35°

Answer key

  1. 150°
  2. 90°
  3. 150°
  4. 75°
  5. 10°
  6. 60°
  7. 140°
  8. 80°
  9. 145°
  10. 115°
  11. 95°
  12. 25°
  13. 30°
  14. 90°
  15. 50°
  16. 135°
  17. 135°
  18. 85°
  19. 25°
  20. 55°
  21. 100°
  22. 145°
  23. 75°
  24. 95°
  25. 90°
  26. 80°
  27. 65°
  28. 85°
  29. 75°
  30. 90°
  31. 120°
  32. 100°
  33. 60°
  34. 95°
  35. 110°
  36. 110°
  37. 125°
  38. 80°
  39. 20°
  40. 35°

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