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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 805 · 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 angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 55° (d) 20°
  2. 2.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 130° (d) 150°
  3. 3.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 50°
  4. 4.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
  6. 6.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 60° (c) 120° (d) 115°
  7. 7.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) 35° (c) 55° (d) 125°
  8. 8.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 110° (b) 145° (c) 75° (d) 105°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 240° (d) 121°
  11. 11.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 80° (b) 135° (c) 145° (d) 100°
  12. 12.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 91° (c) 45° (d) 135°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 30° (d) 40°
  14. 14.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
  17. 17.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) 40° (c) 310° (d) 130°
  18. 18.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
  20. 20.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 95° (d) 85°
  21. 21.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 100° (c) 150° (d) 110°
  22. 22.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 50° (d) 130°
  24. 24.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 75° (b) 105° (c) 155° (d) 130°
  25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 140° (d) 50°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 150° (c) 75° (d) 105°
  27. 27.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 80° (b) 110° (c) 150° (d) 100°
  28. 28.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 165° (c) 16° (d) 15°
  29. 29.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 35° (c) 110° (d) 145°
  30. 30.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 160° (c) 270° (d) 90°
  31. 31.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 140° (b) 165° (c) 55° (d) 15°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 55° (d) 46°
  33. 33.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 35° (d) 215°
  34. 34.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 75° (d) 155°
  35. 35.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 125° (d) 140°
  36. 36.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 155° (c) 65° (d) 25°
  37. 37.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 75°
  38. 38.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°
  39. 39.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 65° (b) 145° (c) 115° (d) 100°
  40. 40.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 145° (c) 270° (d) 90°

Answer key

  1. 55°
  2. 80°
  3. 50°
  4. 40°
  5. 35°
  6. 120°
  7. 125°
  8. 75°
  9. 75°
  10. 120°
  11. 100°
  12. 90°
  13. 20°
  14. 50°
  15. 60°
  16. 50°
  17. 130°
  18. 110°
  19. 70°
  20. 10°
  21. 150°
  22. 150°
  23. 130°
  24. 105°
  25. 100°
  26. 75°
  27. 80°
  28. 15°
  29. 35°
  30. 90°
  31. 15°
  32. 45°
  33. 145°
  34. 130°
  35. 95°
  36. 155°
  37. 75°
  38. 130°
  39. 65°
  40. 90°

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