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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 127 · 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 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 65° (d) 130°
  2. 2.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 30° (b) 80° (c) 150° (d) 130°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
  4. 4.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
  5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  6. 6.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 85° (d) 95°
  7. 7.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 155° (d) 65°
  8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  10. 10.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 60° (c) 155° (d) 120°
  11. 11.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 31° (d) 30°
  12. 12.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 145° (d) 65°
  13. 13.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 85°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 80° (d) 140°
  15. 15.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
  16. 16.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 45° (d) 225°
  17. 17.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 310° (c) 130° (d) 50°
  18. 18.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 55° (c) 145° (d) 160°
  19. 19.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 100° (c) 115° (d) 145°
  20. 20.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 110° (c) 45° (d) 115°
  21. 21.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 120° (c) 155° (d) 95°
  22. 22.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 170° (c) 105° (d) 10°
  23. 23.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 320° (b) 40° (c) 160° (d) 140°
  24. 24.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 160° (d) 20°
  26. 26.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
  27. 27.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 270°
  28. 28.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 150° (c) 125° (d) 55°
  29. 29.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 100° (d) 140°
  30. 30.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 60° (d) 120°
  31. 31.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 115°
  32. 32.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 155°
  33. 33.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 65° (b) 140° (c) 155° (d) 40°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 10° (d) 20°
  35. 35.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 65°
  36. 36.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 105° (b) 80° (c) 155° (d) 100°
  37. 37.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 80° (d) 100°
  38. 38.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 80°
  39. 39.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 65° (b) 170° (c) 125° (d) 10°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°

Answer key

  1. 65°
  2. 150°
  3. 80°
  4. 30°
  5. 120°
  6. 95°
  7. 65°
  8. 110°
  9. 80°
  10. 60°
  11. 30°
  12. 65°
  13. 85°
  14. 40°
  15. 10°
  16. 45°
  17. 50°
  18. 125°
  19. 35°
  20. 45°
  21. 95°
  22. 10°
  23. 140°
  24. 40°
  25. 160°
  26. 85°
  27. 90°
  28. 125°
  29. 100°
  30. 60°
  31. 80°
  32. 115°
  33. 40°
  34. 10°
  35. 65°
  36. 80°
  37. 20°
  38. 80°
  39. 10°
  40. 25°

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