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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 511 · 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 80°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
  2. 2.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 155° (d) 30°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 46°
  4. 4.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 145° (d) 40°
  5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°
  6. 6.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) 265° (c) 85° (d) 95°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 110° (c) 70° (d) 140°
  8. 8.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 125° (b) 80° (c) 100° (d) 155°
  9. 9.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 60°
  10. 10.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 135° (d) 110°
  11. 11.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 120° (b) 45° (c) 135° (d) 105°
  12. 12.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 70°
  13. 13.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 80°
  14. 14.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 45° (d) 135°
  15. 15.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 160° (c) 110° (d) 270°
  16. 16.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 135° (b) 95° (c) 50° (d) 130°
  17. 17.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 215° (c) 145° (d) 36°
  18. 18.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 80° (c) 115° (d) 100°
  19. 19.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 155° (d) 310°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 40° (d) 60°
  21. 21.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 155° (c) 95° (d) 85°
  22. 22.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 140° (b) 60° (c) 160° (d) 120°
  23. 23.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 130° (c) 50° (d) 140°
  24. 24.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 110° (d) 70°
  25. 25.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) 280° (c) 100° (d) 10°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
  27. 27.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 35° (b) 155° (c) 10° (d) 170°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 110° (d) 145°
  29. 29.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 120°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 160° (d) 20°
  31. 31.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 25°
  32. 32.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 120° (b) 125° (c) 60° (d) 115°
  33. 33.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 100° (c) 30° (d) 150°
  34. 34.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 20° (d) 160°
  35. 35.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 160° (b) 165° (c) 35° (d) 15°
  36. 36.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 290° (c) 70° (d) 145°
  37. 37.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 125° (c) 10° (d) 65°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
  39. 39.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 90° (c) 270° (d) 125°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 140° (c) 160° (d) 320°

Answer key

  1. 30°
  2. 150°
  3. 45°
  4. 140°
  5. 130°
  6. 85°
  7. 70°
  8. 100°
  9. 60°
  10. 135°
  11. 135°
  12. 70°
  13. 100°
  14. 135°
  15. 90°
  16. 50°
  17. 35°
  18. 80°
  19. 50°
  20. 30°
  21. 95°
  22. 120°
  23. 130°
  24. 70°
  25. 100°
  26. 45°
  27. 10°
  28. 145°
  29. 105°
  30. 10°
  31. 25°
  32. 60°
  33. 30°
  34. 20°
  35. 15°
  36. 70°
  37. 10°
  38. 130°
  39. 90°
  40. 160°

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