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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 159 · 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 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
  2. 2.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 115° (d) 25°
  3. 3.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) 40° (d) 30°
  4. 4.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 110° (d) 85°
  5. 5.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 75° (b) 140° (c) 115° (d) 105°
  6. 6.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 150° (c) 95° (d) 85°
  7. 7.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
  8. 8.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 145° (d) 110°
  9. 9.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 145° (d) 35°
  10. 10.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 130° (b) 50° (c) 140° (d) 90°
  11. 11.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 200° (d) 160°
  12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 55° (d) 70°
  13. 13.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 50° (c) 120° (d) 130°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 26° (c) 25° (d) 155°
  15. 15.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 125° (c) 80° (d) 100°
  16. 16.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 310° (c) 130° (d) 50°
  17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  18. 18.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 70° (c) 155° (d) 135°
  19. 19.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 255° (c) 105° (d) 150°
  20. 20.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 55° (b) 125° (c) 110° (d) 235°
  21. 21.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 100°
  22. 22.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 160° (b) 85° (c) 115° (d) 95°
  23. 23.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 55° (c) 150° (d) 155°
  24. 24.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  25. 25.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 145° (c) 115° (d) 150°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 120° (d) 60°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 120° (d) 121°
  28. 28.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 165° (b) 70° (c) 15° (d) 125°
  29. 29.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 85° (d) 140°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 15° (c) 165° (d) 30°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
  32. 32.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 30° (d) 80°
  33. 33.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 85° (b) 115° (c) 160° (d) 65°
  34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
  35. 35.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 120°
  36. 36.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 135° (c) 125° (d) 100°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 320° (d) 20°
  38. 38.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 140° (c) 40° (d) 41°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 36° (c) 70° (d) 35°
  40. 40.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 95° (d) 85°

Answer key

  1. 35°
  2. 115°
  3. 20°
  4. 15°
  5. 75°
  6. 95°
  7. 100°
  8. 145°
  9. 145°
  10. 50°
  11. 20°
  12. 70°
  13. 130°
  14. 25°
  15. 80°
  16. 50°
  17. 50°
  18. 135°
  19. 105°
  20. 55°
  21. 100°
  22. 95°
  23. 150°
  24. 30°
  25. 115°
  26. 60°
  27. 120°
  28. 15°
  29. 85°
  30. 15°
  31. 65°
  32. 150°
  33. 65°
  34. 110°
  35. 120°
  36. 80°
  37. 160°
  38. 40°
  39. 35°
  40. 85°

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