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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 279 · 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 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 40° (d) 50°
  2. 2.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 155° (b) 20° (c) 160° (d) 45°
  3. 3.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 65° (b) 115° (c) 140° (d) 155°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  5. 5.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 40° (c) 140° (d) 320°
  6. 6.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°
  7. 7.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
  8. 8.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 125° (c) 145° (d) 90°
  9. 9.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 45° (d) 135°
  10. 10.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 30° (b) 80° (c) 130° (d) 150°
  11. 11.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 210° (b) 60° (c) 30° (d) 150°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 170° (d) 20°
  13. 13.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 155° (c) 160° (d) 135°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
  15. 15.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 160° (d) 20°
  16. 16.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 160° (d) 340°
  17. 17.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 100° (c) 115° (d) 145°
  18. 18.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 135° (b) 155° (c) 70° (d) 110°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 110° (c) 71° (d) 70°
  20. 20.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 150° (c) 30° (d) 50°
  21. 21.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 10° (c) 50° (d) 170°
  22. 22.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 115° (b) 100° (c) 80° (d) 145°
  23. 23.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 110° (b) 100° (c) 70° (d) 150°
  24. 24.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 190° (c) 11° (d) 170°
  25. 25.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 105° (d) 130°
  26. 26.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 135° (c) 115° (d) 65°
  27. 27.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 275° (c) 95° (d) 85°
  28. 28.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 120° (d) 140°
  29. 29.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 120° (c) 145° (d) 60°
  30. 30.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 130° (b) 140° (c) 270° (d) 90°
  31. 31.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 95° (d) 160°
  32. 32.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  33. 33.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 105° (c) 155° (d) 100°
  34. 34.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 80° (d) 130°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
  36. 36.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°
  37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 35° (d) 50°
  39. 39.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) 60° (d) 61°
  40. 40.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°

Answer key

  1. 40°
  2. 20°
  3. 115°
  4. 60°
  5. 40°
  6. 25°
  7. 60°
  8. 90°
  9. 90°
  10. 150°
  11. 150°
  12. 10°
  13. 135°
  14. 70°
  15. 20°
  16. 160°
  17. 35°
  18. 110°
  19. 70°
  20. 30°
  21. 10°
  22. 80°
  23. 70°
  24. 10°
  25. 75°
  26. 115°
  27. 95°
  28. 140°
  29. 120°
  30. 90°
  31. 105°
  32. 30°
  33. 80°
  34. 80°
  35. 35°
  36. 55°
  37. 130°
  38. 25°
  39. 60°
  40. 50°

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