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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 108 · 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.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 80° (d) 130°
  3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
  4. 4.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 70° (c) 110° (d) 20°
  5. 5.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 140° (b) 120° (c) 160° (d) 60°
  6. 6.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 60° (d) 121°
  8. 8.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 135°
  9. 9.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 80° (d) 100°
  10. 10.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 65° (b) 110° (c) 135° (d) 115°
  11. 11.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 145° (c) 100° (d) 115°
  12. 12.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 75° (d) 105°
  13. 13.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 90° (c) 120° (d) 150°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 90° (d) 135°
  15. 15.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 165° (c) 15° (d) 115°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 25° (d) 130°
  17. 17.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 100° (d) 145°
  18. 18.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 100° (d) 30°
  19. 19.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 60°
  20. 20.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 45° (c) 135° (d) 100°
  21. 21.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 160° (d) 145°
  22. 22.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 135° (c) 170° (d) 10°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 170° (c) 11° (d) 10°
  24. 24.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 85° (c) 145° (d) 130°
  25. 25.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 70° (b) 95° (c) 155° (d) 110°
  26. 26.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 30° (d) 150°
  27. 27.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
  28. 28.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 30° (b) 145° (c) 65° (d) 150°
  29. 29.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 35° (c) 145° (d) 36°
  30. 30.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 145° (c) 85° (d) 95°
  31. 31.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 155° (c) 65° (d) 115°
  32. 32.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
  33. 33.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
  34. 34.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 125° (d) 115°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 220° (d) 110°
  36. 36.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 245° (c) 115° (d) 65°
  37. 37.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 56° (d) 235°
  38. 38.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 85° (b) 135° (c) 95° (d) 140°
  39. 39.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 310° (d) 130°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°

Answer key

  1. 10°
  2. 130°
  3. 50°
  4. 110°
  5. 120°
  6. 125°
  7. 120°
  8. 75°
  9. 100°
  10. 65°
  11. 65°
  12. 105°
  13. 120°
  14. 135°
  15. 15°
  16. 25°
  17. 115°
  18. 150°
  19. 60°
  20. 45°
  21. 55°
  22. 10°
  23. 10°
  24. 145°
  25. 70°
  26. 150°
  27. 60°
  28. 150°
  29. 35°
  30. 85°
  31. 65°
  32. 145°
  33. 10°
  34. 120°
  35. 110°
  36. 65°
  37. 55°
  38. 95°
  39. 130°
  40. 35°

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