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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 178 · 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 65° and 80°. What is the third angle? (a) 145° (b) 100° (c) 35° (d) 115°
  2. 2.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 125° (b) 160° (c) 75° (d) 105°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 30° (d) 140°
  4. 4.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  5. 5.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 95° (c) 85° (d) 145°
  6. 6.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 130° (c) 50° (d) 230°
  7. 7.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 65° (b) 115° (c) 90° (d) 155°
  8. 8.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 325° (d) 55°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  11. 11.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 91° (d) 135°
  12. 12.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 105° (d) 145°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 71° (d) 70°
  14. 14.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 75° (c) 110° (d) 145°
  15. 15.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 30° (c) 80° (d) 150°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 105° (d) 150°
  17. 17.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 65° (b) 140° (c) 155° (d) 25°
  18. 18.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 40° (c) 15° (d) 155°
  19. 19.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 30° (c) 150° (d) 145°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 55° (c) 250° (d) 70°
  21. 21.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  23. 23.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 136° (c) 45° (d) 315°
  24. 24.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 80° (d) 100°
  25. 25.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 145° (d) 110°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 95° (d) 86°
  27. 27.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 110° (c) 70° (d) 150°
  28. 28.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 80° (d) 135°
  29. 29.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 65° (c) 50° (d) 230°
  31. 31.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 80° (c) 120° (d) 160°
  32. 32.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 165° (c) 145° (d) 15°
  33. 33.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
  34. 34.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 70° (b) 110° (c) 115° (d) 135°
  35. 35.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 240° (c) 61° (d) 60°
  36. 36.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 60° (c) 120° (d) 140°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 70° (d) 120°
  38. 38.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) 95° (c) 85° (d) 265°
  39. 39.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 135° (d) 45°
  40. 40.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 115° (d) 110°

Answer key

  1. 35°
  2. 105°
  3. 20°
  4. 10°
  5. 85°
  6. 50°
  7. 65°
  8. 145°
  9. 65°
  10. 80°
  11. 90°
  12. 105°
  13. 70°
  14. 75°
  15. 150°
  16. 75°
  17. 25°
  18. 15°
  19. 150°
  20. 125°
  21. 130°
  22. 45°
  23. 135°
  24. 80°
  25. 110°
  26. 85°
  27. 70°
  28. 80°
  29. 120°
  30. 115°
  31. 120°
  32. 15°
  33. 70°
  34. 70°
  35. 60°
  36. 120°
  37. 60°
  38. 85°
  39. 135°
  40. 135°

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