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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 656 · 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 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
  2. 2.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 100° (d) 80°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 45° (d) 110°
  4. 4.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 160° (d) 155°
  5. 5.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 115° (b) 140° (c) 155° (d) 65°
  6. 6.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 90° (c) 270° (d) 160°
  7. 7.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 275° (d) 95°
  8. 8.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 130° (d) 50°
  9. 9.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) 135° (d) 136°
  10. 10.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
  11. 11.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 45° (d) 115°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 40° (d) 140°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
  15. 15.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 145° (b) 90° (c) 125° (d) 35°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 90° (d) 46°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 80° (c) 50° (d) 100°
  18. 18.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 80° (d) 100°
  19. 19.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 100° (c) 80° (d) 160°
  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.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 230° (b) 130° (c) 115° (d) 50°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 60° (d) 59°
  23. 23.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 155° (d) 25°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 130° (d) 310°
  25. 25.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 130°
  26. 26.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 130° (c) 145° (d) 85°
  27. 27.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 145° (b) 30° (c) 65° (d) 150°
  28. 28.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 260° (d) 80°
  29. 29.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 130° (c) 95° (d) 85°
  30. 30.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 110° (c) 145° (d) 105°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
  32. 32.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 90° (c) 140° (d) 130°
  33. 33.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 145° (b) 120° (c) 85° (d) 95°
  34. 34.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 55° (d) 100°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
  36. 36.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 160° (d) 110°
  37. 37.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
  38. 38.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 35°
  39. 39.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 105° (c) 210° (d) 150°
  40. 40.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 135° (c) 155° (d) 160°

Answer key

  1. 100°
  2. 20°
  3. 35°
  4. 45°
  5. 115°
  6. 90°
  7. 95°
  8. 130°
  9. 135°
  10. 130°
  11. 135°
  12. 70°
  13. 20°
  14. 75°
  15. 35°
  16. 45°
  17. 50°
  18. 80°
  19. 100°
  20. 125°
  21. 50°
  22. 60°
  23. 155°
  24. 155°
  25. 50°
  26. 145°
  27. 30°
  28. 80°
  29. 85°
  30. 75°
  31. 50°
  32. 90°
  33. 85°
  34. 125°
  35. 65°
  36. 90°
  37. 35°
  38. 145°
  39. 150°
  40. 135°

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