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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 508 · 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 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
  2. 2.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 85° (d) 120°
  3. 3.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 20° (d) 160°
  4. 4.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 80° (c) 135° (d) 100°
  5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
  6. 6.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 45° (c) 135° (d) 100°
  7. 7.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 80° (b) 130° (c) 100° (d) 260°
  8. 8.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 40° (d) 140°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
  10. 10.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 110° (b) 135° (c) 45° (d) 115°
  11. 11.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 155° (b) 125° (c) 100° (d) 80°
  12. 12.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 90° (b) 135° (c) 91° (d) 270°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 160°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 145° (c) 35° (d) 290°
  15. 15.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 235° (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) 105° (b) 76° (c) 255° (d) 75°
  17. 17.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 75° (b) 130° (c) 105° (d) 155°
  18. 18.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  19. 19.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 130° (d) 50°
  20. 20.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 90° (c) 140° (d) 130°
  21. 21.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°
  22. 22.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 100° (c) 230° (d) 50°
  23. 23.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 55° (b) 105° (c) 130° (d) 125°
  24. 24.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) 30° (d) 20°
  25. 25.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 150° (d) 85°
  26. 26.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 60° (b) 125° (c) 115° (d) 120°
  27. 27.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 195° (d) 165°
  28. 28.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 40° (c) 80° (d) 140°
  29. 29.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) 155° (c) 65° (d) 335°
  30. 30.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 40° (c) 20° (d) 70°
  31. 31.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 115° (b) 125° (c) 120° (d) 55°
  32. 32.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 160°
  33. 33.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 60° (d) 120°
  34. 34.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) 325° (d) 35°
  35. 35.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 230° (c) 100° (d) 50°
  36. 36.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 36° (c) 145° (d) 35°
  39. 39.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 150° (d) 50°
  40. 40.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 95° (d) 140°

Answer key

  1. 80°
  2. 95°
  3. 160°
  4. 80°
  5. 110°
  6. 135°
  7. 80°
  8. 40°
  9. 40°
  10. 45°
  11. 100°
  12. 90°
  13. 10°
  14. 145°
  15. 55°
  16. 75°
  17. 105°
  18. 10°
  19. 130°
  20. 90°
  21. 100°
  22. 50°
  23. 55°
  24. 20°
  25. 95°
  26. 60°
  27. 15°
  28. 40°
  29. 155°
  30. 40°
  31. 55°
  32. 105°
  33. 120°
  34. 145°
  35. 50°
  36. 100°
  37. 140°
  38. 35°
  39. 50°
  40. 85°

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