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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 287 · 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) 40° (b) 100° (c) 140° (d) 50°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
  3. 3.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 135° (d) 75°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
  5. 5.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 305° (c) 35° (d) 125°
  6. 6.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°
  7. 7.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 85° (b) 20° (c) 115° (d) 160°
  8. 8.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 30° (d) 31°
  9. 9.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 120° (b) 125° (c) 65° (d) 115°
  10. 10.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 50° (c) 140° (d) 130°
  11. 11.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  13. 13.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  14. 14.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
  15. 15.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 100° (d) 110°
  16. 16.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 95° (c) 140° (d) 135°
  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) 145° (b) 35° (c) 36° (d) 215°
  18. 18.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 215° (b) 35° (c) 145° (d) 70°
  19. 19.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 105° (c) 95° (d) 75°
  20. 20.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 155° (b) 115° (c) 90° (d) 270°
  21. 21.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 95° (b) 85° (c) 120° (d) 145°
  22. 22.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 120° (d) 30°
  23. 23.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 55° (d) 125°
  24. 24.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 80° (d) 260°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 130° (d) 40°
  26. 26.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 150° (c) 80° (d) 50°
  27. 27.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 70° (d) 110°
  28. 28.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 155° (d) 90°
  29. 29.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
  30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  31. 31.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 220° (c) 41° (d) 140°
  32. 32.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 95° (c) 85° (d) 125°
  33. 33.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 75° (d) 145°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 40° (c) 140° (d) 30°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
  36. 36.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 160° (b) 120° (c) 100° (d) 80°
  37. 37.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 70° (b) 140° (c) 250° (d) 110°
  38. 38.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 100° (c) 230° (d) 50°
  39. 39.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 15° (d) 165°
  40. 40.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 160° (c) 110° (d) 20°

Answer key

  1. 100°
  2. 80°
  3. 75°
  4. 85°
  5. 125°
  6. 135°
  7. 20°
  8. 30°
  9. 65°
  10. 130°
  11. 90°
  12. 125°
  13. 110°
  14. 130°
  15. 100°
  16. 95°
  17. 35°
  18. 35°
  19. 75°
  20. 90°
  21. 85°
  22. 120°
  23. 55°
  24. 80°
  25. 65°
  26. 50°
  27. 70°
  28. 90°
  29. 135°
  30. 80°
  31. 40°
  32. 95°
  33. 105°
  34. 20°
  35. 75°
  36. 100°
  37. 70°
  38. 50°
  39. 15°
  40. 20°

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