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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 354 · 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 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 115° (d) 95°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
  3. 3.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 120° (b) 100° (c) 160° (d) 80°
  4. 4.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 160° (b) 65° (c) 135° (d) 45°
  5. 5.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 130° (d) 50°
  6. 6.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 30° (d) 150°
  7. 7.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 110° (b) 130° (c) 70° (d) 160°
  8. 8.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 160° (c) 80° (d) 100°
  9. 9.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 145°
  10. 10.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 100° (d) 80°
  11. 11.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  12. 12.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 295° (d) 115°
  13. 13.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 100° (c) 155° (d) 105°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 56° (c) 55° (d) 110°
  16. 16.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 65°
  17. 17.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 140° (d) 110°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 270° (d) 90°
  21. 21.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  22. 22.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) 50° (d) 40°
  23. 23.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 120° (d) 35°
  24. 24.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 125° (b) 85° (c) 30° (d) 150°
  25. 25.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 75° (d) 150°
  26. 26.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 130° (d) 110°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  28. 28.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 220° (b) 40° (c) 140° (d) 80°
  29. 29.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 30° (b) 120° (c) 90° (d) 150°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 50° (c) 115° (d) 230°
  31. 31.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 160° (b) 70° (c) 50° (d) 130°
  32. 32.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 110° (b) 120° (c) 70° (d) 130°
  33. 33.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
  34. 34.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 35° (c) 165° (d) 160°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 31° (c) 150° (d) 60°
  37. 37.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 45°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 40° (d) 20°
  39. 39.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 40° (b) 155° (c) 140° (d) 65°
  40. 40.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 155° (c) 125° (d) 55°

Answer key

  1. 95°
  2. 70°
  3. 100°
  4. 135°
  5. 130°
  6. 150°
  7. 110°
  8. 80°
  9. 75°
  10. 100°
  11. 120°
  12. 115°
  13. 25°
  14. 50°
  15. 55°
  16. 65°
  17. 110°
  18. 95°
  19. 10°
  20. 135°
  21. 130°
  22. 40°
  23. 145°
  24. 30°
  25. 75°
  26. 70°
  27. 100°
  28. 140°
  29. 30°
  30. 115°
  31. 50°
  32. 70°
  33. 50°
  34. 15°
  35. 85°
  36. 30°
  37. 135°
  38. 20°
  39. 40°
  40. 55°

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