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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 119 · 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 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 55° (d) 46°
  2. 2.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 95° (d) 150°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
  4. 4.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 20° (c) 160° (d) 110°
  5. 5.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 50° (b) 230° (c) 130° (d) 100°
  6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
  7. 7.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
  10. 10.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 90° (c) 270° (d) 130°
  11. 11.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 70°
  12. 12.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 325° (d) 145°
  13. 13.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 155° (d) 115°
  14. 14.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
  15. 15.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 130° (c) 50° (d) 150°
  16. 16.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 150° (b) 90° (c) 270° (d) 120°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 10° (d) 20°
  18. 18.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 135° (b) 70° (c) 155° (d) 25°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  20. 20.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 100° (d) 80°
  21. 21.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 100° (b) 130° (c) 260° (d) 80°
  22. 22.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°
  23. 23.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 290° (c) 110° (d) 70°
  24. 24.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 75° (d) 105°
  25. 25.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  26. 26.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 225° (b) 90° (c) 135° (d) 45°
  27. 27.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 115° (b) 125° (c) 120° (d) 60°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 70° (d) 160°
  29. 29.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 90° (d) 91°
  30. 30.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 230° (d) 130°
  31. 31.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 45° (d) 115°
  32. 32.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 35° (d) 95°
  33. 33.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 60° (b) 85° (c) 120° (d) 155°
  34. 34.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 55° (d) 70°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 80° (d) 50°
  36. 36.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 61° (b) 120° (c) 240° (d) 60°
  37. 37.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) 65° (c) 115° (d) 245°
  38. 38.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 85°
  39. 39.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 85° (d) 125°
  40. 40.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 95° (c) 105° (d) 85°

Answer key

  1. 45°
  2. 30°
  3. 15°
  4. 20°
  5. 50°
  6. 10°
  7. 20°
  8. 25°
  9. 35°
  10. 90°
  11. 110°
  12. 145°
  13. 115°
  14. 120°
  15. 130°
  16. 90°
  17. 10°
  18. 25°
  19. 35°
  20. 80°
  21. 80°
  22. 35°
  23. 110°
  24. 105°
  25. 50°
  26. 135°
  27. 60°
  28. 80°
  29. 90°
  30. 130°
  31. 135°
  32. 145°
  33. 120°
  34. 70°
  35. 40°
  36. 60°
  37. 65°
  38. 95°
  39. 125°
  40. 85°

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