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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 316 · 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 20° and 25°. What is the third angle? (a) 135° (b) 155° (c) 160° (d) 45°
  2. 2.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 120°
  3. 3.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 140° (c) 40° (d) 100°
  4. 4.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 55° (d) 35°
  5. 5.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 35° (c) 100° (d) 115°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 10° (c) 11° (d) 20°
  7. 7.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 155° (d) 105°
  8. 8.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 105° (d) 110°
  9. 9.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 145° (d) 55°
  10. 10.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 65° (d) 25°
  11. 11.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 100° (b) 200° (c) 20° (d) 160°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
  13. 13.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 170° (b) 90° (c) 100° (d) 10°
  14. 14.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 150° (c) 45° (d) 75°
  15. 15.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 130° (c) 50° (d) 230°
  16. 16.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 140° (d) 155°
  17. 17.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 150° (b) 60° (c) 90° (d) 120°
  18. 18.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 105° (c) 120° (d) 60°
  19. 19.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) 170° (c) 10° (d) 190°
  20. 20.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 230° (c) 50° (d) 130°
  21. 21.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 90° (b) 120° (c) 270° (d) 150°
  22. 22.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 140° (d) 100°
  23. 23.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 85° (c) 95° (d) 155°
  24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  25. 25.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 130° (d) 120°
  26. 26.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 220° (c) 110° (d) 40°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 30° (c) 15° (d) 165°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 160° (d) 70°
  29. 29.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 325° (c) 35° (d) 55°
  30. 30.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 65° (d) 100°
  31. 31.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 330° (d) 30°
  32. 32.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 130° (b) 95° (c) 85° (d) 135°
  33. 33.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 85° (d) 145°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 80° (d) 100°
  35. 35.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 80°
  36. 36.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 145° (d) 120°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
  38. 38.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 80° (c) 40° (d) 140°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 145° (c) 290° (d) 110°
  40. 40.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 300° (d) 120°

Answer key

  1. 135°
  2. 40°
  3. 40°
  4. 70°
  5. 35°
  6. 10°
  7. 75°
  8. 105°
  9. 110°
  10. 115°
  11. 20°
  12. 25°
  13. 10°
  14. 135°
  15. 130°
  16. 65°
  17. 60°
  18. 60°
  19. 10°
  20. 130°
  21. 90°
  22. 120°
  23. 95°
  24. 20°
  25. 120°
  26. 140°
  27. 15°
  28. 80°
  29. 145°
  30. 115°
  31. 150°
  32. 85°
  33. 85°
  34. 40°
  35. 80°
  36. 95°
  37. 35°
  38. 40°
  39. 145°
  40. 120°

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