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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 971 · 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 two equal angles are 80° each. What is the third angle? (a) 100° (b) 20° (c) 80° (d) 10°
  2. 2.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 65° (d) 135°
  3. 3.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 110° (d) 20°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 85° (c) 95° (d) 190°
  5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  6. 6.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 65° (d) 155°
  7. 7.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 25°
  8. 8.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
  9. 9.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 110° (d) 70°
  10. 10.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 120° (b) 140° (c) 40° (d) 100°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 80° (c) 81° (d) 160°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 240° (d) 60°
  13. 13.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 155° (d) 100°
  14. 14.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 220° (b) 110° (c) 140° (d) 40°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
  16. 16.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 70° (d) 110°
  17. 17.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 65° (d) 145°
  18. 18.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 110° (b) 150° (c) 70° (d) 100°
  19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  20. 20.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 130° (b) 135° (c) 95° (d) 85°
  21. 21.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
  22. 22.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) 225° (c) 135° (d) 45°
  23. 23.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 155° (c) 100° (d) 105°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 35° (c) 36° (d) 70°
  25. 25.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 130° (c) 85° (d) 35°
  26. 26.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 56° (d) 235°
  27. 27.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 75° (c) 15° (d) 105°
  28. 28.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 85°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 65° (c) 115° (d) 230°
  30. 30.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 100° (b) 150° (c) 30° (d) 110°
  31. 31.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) 50° (d) 40°
  32. 32.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 110° (d) 250°
  33. 33.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 155° (d) 105°
  34. 34.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 90° (b) 270° (c) 115° (d) 155°
  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) 130° (c) 155° (d) 310°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  37. 37.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 100° (d) 35°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 40°
  39. 39.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 65° (b) 40° (c) 140° (d) 155°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 160° (c) 40° (d) 20°

Answer key

  1. 20°
  2. 115°
  3. 40°
  4. 95°
  5. 10°
  6. 130°
  7. 25°
  8. 85°
  9. 70°
  10. 40°
  11. 80°
  12. 120°
  13. 105°
  14. 140°
  15. 65°
  16. 70°
  17. 65°
  18. 70°
  19. 100°
  20. 85°
  21. 50°
  22. 45°
  23. 80°
  24. 35°
  25. 145°
  26. 55°
  27. 105°
  28. 85°
  29. 115°
  30. 30°
  31. 70°
  32. 70°
  33. 75°
  34. 90°
  35. 155°
  36. 80°
  37. 145°
  38. 30°
  39. 40°
  40. 20°

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