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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 412 · 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 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 40° (d) 50°
  2. 2.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 260° (d) 160°
  3. 3.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 11° (c) 10° (d) 170°
  4. 4.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 140° (c) 105° (d) 145°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 20° (d) 160°
  6. 6.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 150° (b) 30° (c) 135° (d) 75°
  7. 7.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) 30° (d) 60°
  8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
  9. 9.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 65° (d) 115°
  10. 10.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 140° (d) 105°
  11. 11.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 60° (b) 20° (c) 160° (d) 140°
  12. 12.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 15° (c) 165° (d) 65°
  13. 13.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 65°
  14. 14.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 110° (d) 160°
  15. 15.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°
  16. 16.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 30°
  17. 17.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
  20. 20.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 145° (b) 160° (c) 35° (d) 55°
  21. 21.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 95° (b) 105° (c) 85° (d) 160°
  22. 22.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 30° (d) 150°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°
  24. 24.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 135° (d) 125°
  25. 25.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 80° (d) 100°
  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) 135° (b) 136° (c) 45° (d) 315°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 120° (d) 60°
  28. 28.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 145° (b) 25° (c) 60° (d) 155°
  29. 29.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 195° (c) 165° (d) 16°
  30. 30.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) 46° (d) 55°
  31. 31.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 110° (d) 30°
  32. 32.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 50° (b) 140° (c) 170° (d) 10°
  33. 33.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 130°
  34. 34.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°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
  37. 37.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 115° (c) 65° (d) 125°
  38. 38.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 105° (d) 100°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 110° (d) 145°
  40. 40.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 75° (c) 105° (d) 160°

Answer key

  1. 70°
  2. 100°
  3. 10°
  4. 105°
  5. 80°
  6. 30°
  7. 30°
  8. 100°
  9. 115°
  10. 105°
  11. 20°
  12. 15°
  13. 115°
  14. 90°
  15. 25°
  16. 30°
  17. 90°
  18. 35°
  19. 40°
  20. 35°
  21. 85°
  22. 150°
  23. 15°
  24. 100°
  25. 20°
  26. 135°
  27. 60°
  28. 25°
  29. 15°
  30. 45°
  31. 150°
  32. 10°
  33. 95°
  34. 60°
  35. 10°
  36. 10°
  37. 65°
  38. 100°
  39. 145°
  40. 105°

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