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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 183 · 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. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 80° (d) 50°
  3. 3.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 55° (d) 100°
  4. 4.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 145° (c) 125° (d) 90°
  5. 5.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 65° (d) 45°
  6. 6.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 90° (b) 155° (c) 270° (d) 115°
  7. 7.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 160° (b) 155° (c) 45° (d) 135°
  8. 8.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 150° (c) 25° (d) 55°
  9. 9.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°
  10. 10.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 95° (d) 105°
  11. 11.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 45° (d) 90°
  12. 12.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 10° (c) 280° (d) 80°
  13. 13.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 55° (d) 145°
  14. 14.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 160° (d) 135°
  15. 15.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 55° (b) 125° (c) 115° (d) 120°
  16. 16.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 255° (d) 75°
  17. 17.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 60°
  18. 18.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 150°
  19. 19.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 65° (b) 135° (c) 115° (d) 110°
  20. 20.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) 320° (d) 160°
  21. 21.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 50° (d) 51°
  22. 22.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
  23. 23.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 155° (b) 50° (c) 75° (d) 130°
  24. 24.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 30° (d) 100°
  25. 25.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 160° (c) 140° (d) 120°
  26. 26.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 50° (d) 80°
  27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 65° (d) 25°
  28. 28.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 45° (c) 135° (d) 46°
  29. 29.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 80° (c) 81° (d) 100°
  30. 30.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 35° (c) 65° (d) 145°
  31. 31.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 150° (d) 160°
  32. 32.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 60° (d) 100°
  33. 33.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
  34. 34.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 160° (b) 125° (c) 55° (d) 145°
  35. 35.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 30° (c) 50° (d) 150°
  36. 36.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 145° (c) 35° (d) 80°
  37. 37.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 30° (d) 150°
  38. 38.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 150° (b) 100° (c) 110° (d) 30°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 105° (d) 75°
  40. 40.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 35°

Answer key

  1. 110°
  2. 40°
  3. 125°
  4. 90°
  5. 135°
  6. 90°
  7. 135°
  8. 25°
  9. 10°
  10. 95°
  11. 90°
  12. 100°
  13. 110°
  14. 45°
  15. 55°
  16. 75°
  17. 60°
  18. 50°
  19. 65°
  20. 160°
  21. 50°
  22. 30°
  23. 50°
  24. 150°
  25. 120°
  26. 80°
  27. 130°
  28. 45°
  29. 80°
  30. 35°
  31. 50°
  32. 120°
  33. 85°
  34. 55°
  35. 150°
  36. 145°
  37. 150°
  38. 30°
  39. 105°
  40. 145°

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