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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 277 · 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 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 80° (d) 260°
  2. 2.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 260° (c) 80° (d) 160°
  3. 3.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 20° (d) 70°
  4. 4.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 110° (d) 290°
  5. 5.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 45° (c) 135° (d) 95°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 150° (d) 75°
  7. 7.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 35° (b) 145° (c) 135° (d) 80°
  8. 8.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 60° (d) 120°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 61° (d) 60°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 140° (c) 280° (d) 100°
  11. 11.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 130°
  12. 12.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 26° (d) 25°
  13. 13.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 135° (d) 75°
  14. 14.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 245° (d) 65°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
  16. 16.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 110° (b) 150° (c) 140° (d) 70°
  17. 17.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 135° (d) 80°
  18. 18.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 40° (d) 115°
  19. 19.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 45° (b) 115° (c) 110° (d) 135°
  20. 20.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 105° (d) 155°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  23. 23.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°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 230° (c) 115° (d) 65°
  25. 25.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 130° (d) 66°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 160° (d) 70°
  28. 28.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 50° (b) 135° (c) 130° (d) 95°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 80° (c) 160° (d) 81°
  30. 30.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 140° (d) 40°
  31. 31.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 35° (d) 325°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 140° (d) 30°
  33. 33.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 130° (c) 160° (d) 110°
  34. 34.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 61°
  35. 35.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 30° (d) 110°
  36. 36.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 160° (d) 260°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
  38. 38.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 100° (b) 115° (c) 145° (d) 65°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 80° (d) 260°
  40. 40.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°

Answer key

  1. 100°
  2. 100°
  3. 40°
  4. 70°
  5. 45°
  6. 75°
  7. 35°
  8. 60°
  9. 60°
  10. 140°
  11. 85°
  12. 25°
  13. 150°
  14. 65°
  15. 15°
  16. 110°
  17. 145°
  18. 140°
  19. 45°
  20. 100°
  21. 40°
  22. 70°
  23. 85°
  24. 115°
  25. 75°
  26. 65°
  27. 80°
  28. 130°
  29. 80°
  30. 140°
  31. 145°
  32. 20°
  33. 70°
  34. 60°
  35. 150°
  36. 100°
  37. 25°
  38. 65°
  39. 130°
  40. 10°

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