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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 289 · 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.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 65°
  2. 2.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 20° (b) 200° (c) 160° (d) 40°
  3. 3.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 45° (c) 100° (d) 135°
  4. 4.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 100° (d) 145°
  5. 5.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 120° (c) 300° (d) 60°
  6. 6.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 50° (c) 150° (d) 20°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 115° (c) 65° (d) 66°
  8. 8.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 135° (c) 136° (d) 45°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 100° (c) 51° (d) 50°
  10. 10.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 145° (b) 100° (c) 65° (d) 115°
  11. 11.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 115° (c) 270° (d) 155°
  12. 12.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 75° (b) 95° (c) 160° (d) 105°
  13. 13.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 45° (d) 135°
  14. 14.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 10° (d) 5°
  15. 15.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 75° (b) 105° (c) 150° (d) 255°
  16. 16.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 115° (b) 50° (c) 230° (d) 130°
  17. 17.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 115° (c) 160° (d) 95°
  18. 18.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) 16° (d) 165°
  19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
  20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
  21. 21.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 165° (b) 55° (c) 15° (d) 140°
  22. 22.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) 25° (c) 155° (d) 205°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
  24. 24.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 55° (d) 155°
  25. 25.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
  26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  27. 27.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 115° (d) 100°
  28. 28.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 140° (d) 125°
  29. 29.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 90° (c) 15° (d) 105°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 50° (d) 130°
  31. 31.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  32. 32.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 80° (d) 100°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 75° (c) 210° (d) 105°
  34. 34.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 125° (b) 95° (c) 55° (d) 140°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 310° (c) 155° (d) 130°
  36. 36.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 130° (b) 75° (c) 105° (d) 155°
  37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
  38. 38.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 30° (b) 65° (c) 150° (d) 145°
  39. 39.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 115° (c) 66° (d) 65°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 25° (d) 130°

Answer key

  1. 115°
  2. 20°
  3. 135°
  4. 80°
  5. 60°
  6. 20°
  7. 65°
  8. 135°
  9. 50°
  10. 65°
  11. 90°
  12. 75°
  13. 45°
  14. 10°
  15. 75°
  16. 50°
  17. 85°
  18. 15°
  19. 100°
  20. 110°
  21. 15°
  22. 25°
  23. 40°
  24. 150°
  25. 85°
  26. 120°
  27. 115°
  28. 95°
  29. 15°
  30. 65°
  31. 70°
  32. 80°
  33. 105°
  34. 55°
  35. 155°
  36. 105°
  37. 130°
  38. 150°
  39. 65°
  40. 25°

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