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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 612 · 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 60° and 35°. What is the third angle? (a) 95° (b) 120° (c) 85° (d) 145°
  3. 3.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 140° (d) 75°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 30° (d) 120°
  5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
  7. 7.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 100° (b) 260° (c) 80° (d) 160°
  8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 40° (d) 130°
  9. 9.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 105° (b) 115° (c) 140° (d) 65°
  10. 10.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 160° (d) 100°
  11. 11.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 80° (d) 100°
  12. 12.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 150° (d) 210°
  13. 13.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 105° (c) 90° (d) 15°
  14. 14.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
  15. 15.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 160° (d) 120°
  16. 16.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°
  17. 17.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 170° (b) 10° (c) 75° (d) 115°
  18. 18.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 90° (d) 30°
  19. 19.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 125° (d) 105°
  20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
  21. 21.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 150° (b) 60° (c) 210° (d) 30°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 36° (d) 145°
  23. 23.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 90° (c) 270° (d) 125°
  24. 24.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) 40° (d) 130°
  25. 25.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 100° (c) 35° (d) 115°
  26. 26.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 35° (c) 215° (d) 70°
  27. 27.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 255° (c) 75° (d) 105°
  28. 28.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 155° (d) 25°
  29. 29.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 45° (b) 150° (c) 75° (d) 135°
  30. 30.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 120° (c) 95° (d) 155°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 60° (d) 150°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
  33. 33.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 65° (d) 25°
  34. 34.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 115° (d) 120°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 30° (d) 120°
  36. 36.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 320° (d) 50°
  37. 37.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 245° (c) 65° (d) 130°
  38. 38.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 80° (b) 100° (c) 125° (d) 155°
  39. 39.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) 30° (d) 140°
  40. 40.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 220° (d) 40°

Answer key

  1. 55°
  2. 85°
  3. 75°
  4. 60°
  5. 110°
  6. 85°
  7. 80°
  8. 80°
  9. 65°
  10. 80°
  11. 100°
  12. 30°
  13. 15°
  14. 60°
  15. 60°
  16. 40°
  17. 10°
  18. 150°
  19. 130°
  20. 30°
  21. 30°
  22. 35°
  23. 90°
  24. 65°
  25. 35°
  26. 35°
  27. 75°
  28. 25°
  29. 45°
  30. 95°
  31. 75°
  32. 35°
  33. 155°
  34. 125°
  35. 30°
  36. 140°
  37. 65°
  38. 100°
  39. 20°
  40. 140°

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