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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 239 · 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 straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 140° (c) 40° (d) 320°
  2. 2.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  3. 3.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 200° (b) 100° (c) 20° (d) 160°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 35° (c) 290° (d) 110°
  5. 5.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 115° (d) 65°
  6. 6.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 255° (c) 105° (d) 75°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 20° (d) 160°
  8. 8.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 115° (d) 145°
  9. 9.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 50° (d) 130°
  10. 10.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 45° (b) 15° (c) 150° (d) 165°
  11. 11.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 260° (c) 100° (d) 130°
  12. 12.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 125° (d) 100°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
  14. 14.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 20° (c) 80° (d) 10°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 46° (d) 55°
  16. 16.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 76° (c) 105° (d) 255°
  17. 17.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 25°
  18. 18.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) 121° (d) 240°
  19. 19.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 260° (c) 50° (d) 80°
  21. 21.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 125° (b) 85° (c) 150° (d) 55°
  22. 22.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°
  23. 23.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 80° (d) 100°
  24. 24.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
  25. 25.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 70° (c) 340° (d) 20°
  26. 26.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 45° (d) 135°
  27. 27.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 100° (b) 130° (c) 50° (d) 230°
  28. 28.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 160° (b) 45° (c) 135° (d) 155°
  29. 29.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 55° (b) 100° (c) 135° (d) 125°
  30. 30.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 65°
  31. 31.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 50° (d) 40°
  32. 32.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 50° (b) 140° (c) 90° (d) 130°
  33. 33.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 125° (b) 100° (c) 55° (d) 135°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 130° (d) 50°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 20° (d) 30°
  36. 36.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 95° (c) 85° (d) 110°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
  38. 38.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 15° (c) 195° (d) 16°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
  40. 40.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°

Answer key

  1. 140°
  2. 130°
  3. 20°
  4. 145°
  5. 65°
  6. 75°
  7. 80°
  8. 65°
  9. 130°
  10. 15°
  11. 100°
  12. 135°
  13. 50°
  14. 20°
  15. 45°
  16. 75°
  17. 25°
  18. 120°
  19. 40°
  20. 130°
  21. 55°
  22. 85°
  23. 100°
  24. 155°
  25. 160°
  26. 135°
  27. 50°
  28. 135°
  29. 125°
  30. 115°
  31. 100°
  32. 50°
  33. 55°
  34. 25°
  35. 20°
  36. 95°
  37. 55°
  38. 15°
  39. 30°
  40. 125°

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