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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 786 · 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 angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 60°
  2. 2.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
  3. 3.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) 100° (c) 80° (d) 81°
  4. 4.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 45° (d) 135°
  5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
  6. 6.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 125° (b) 30° (c) 150° (d) 85°
  7. 7.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 100° (b) 135° (c) 125° (d) 80°
  8. 8.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 120° (c) 115° (d) 125°
  9. 9.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 270° (d) 90°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 70° (c) 36° (d) 35°
  11. 11.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 95° (b) 160° (c) 85° (d) 105°
  12. 12.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 150° (c) 55° (d) 125°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 150° (d) 30°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 105° (c) 30° (d) 75°
  16. 16.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) 135° (c) 45° (d) 46°
  17. 17.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 80° (c) 140° (d) 100°
  18. 18.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 270° (b) 115° (c) 90° (d) 155°
  19. 19.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 110° (b) 95° (c) 155° (d) 70°
  20. 20.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 50° (b) 160° (c) 130° (d) 70°
  21. 21.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 40°
  22. 22.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 50° (d) 80°
  23. 23.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 15° (b) 145° (c) 165° (d) 50°
  24. 24.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 50°
  25. 25.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) 320° (c) 50° (d) 140°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
  27. 27.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 170° (c) 190° (d) 11°
  28. 28.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 300° (b) 150° (c) 60° (d) 120°
  29. 29.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 105° (b) 160° (c) 75° (d) 125°
  30. 30.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 130°
  31. 31.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 145° (c) 115° (d) 65°
  32. 32.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 35°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
  35. 35.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  36. 36.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 135° (d) 55°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 170° (d) 10°
  38. 38.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) 125° (c) 305° (d) 35°
  39. 39.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 130° (c) 90° (d) 270°
  40. 40.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 60° (d) 155°

Answer key

  1. 120°
  2. 110°
  3. 80°
  4. 135°
  5. 120°
  6. 30°
  7. 80°
  8. 125°
  9. 90°
  10. 35°
  11. 85°
  12. 55°
  13. 150°
  14. 75°
  15. 105°
  16. 45°
  17. 80°
  18. 90°
  19. 70°
  20. 130°
  21. 40°
  22. 80°
  23. 15°
  24. 50°
  25. 140°
  26. 45°
  27. 10°
  28. 120°
  29. 105°
  30. 95°
  31. 115°
  32. 35°
  33. 70°
  34. 40°
  35. 10°
  36. 125°
  37. 10°
  38. 125°
  39. 90°
  40. 60°

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