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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 603 · 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 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
  2. 2.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 80° (c) 25° (d) 125°
  3. 3.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 160° (b) 145° (c) 55° (d) 125°
  4. 4.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 160° (c) 90° (d) 270°
  5. 5.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  6. 6.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 160° (d) 20°
  8. 8.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 150° (b) 95° (c) 85° (d) 115°
  9. 9.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 10° (b) 170° (c) 155° (d) 35°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 155° (d) 130°
  11. 11.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 70° (d) 160°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 11° (c) 160° (d) 20°
  13. 13.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 320° (b) 160° (c) 40° (d) 140°
  14. 14.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 40° (c) 125° (d) 95°
  15. 15.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 145° (b) 160° (c) 125° (d) 55°
  16. 16.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 10°
  18. 18.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
  19. 19.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 135°
  20. 20.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 65° (c) 335° (d) 25°
  21. 21.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 105° (b) 75° (c) 125° (d) 130°
  22. 22.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 135°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 120° (d) 150°
  24. 24.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 140°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
  26. 26.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 35° (d) 305°
  27. 27.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 60° (b) 85° (c) 155° (d) 120°
  28. 28.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 30° (c) 61° (d) 120°
  29. 29.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 140° (d) 320°
  30. 30.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 135° (b) 80° (c) 125° (d) 100°
  31. 31.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 10° (b) 100° (c) 170° (d) 90°
  32. 32.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°
  33. 33.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 30° (b) 145° (c) 150° (d) 65°
  34. 34.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 125° (b) 155° (c) 55° (d) 150°
  35. 35.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 60°
  36. 36.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 150° (d) 100°
  37. 37.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 130° (d) 105°
  38. 38.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 105° (b) 45° (c) 120° (d) 135°
  39. 39.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 260° (d) 81°
  40. 40.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°

Answer key

  1. 10°
  2. 25°
  3. 125°
  4. 90°
  5. 100°
  6. 30°
  7. 80°
  8. 85°
  9. 10°
  10. 155°
  11. 110°
  12. 10°
  13. 40°
  14. 40°
  15. 125°
  16. 20°
  17. 50°
  18. 110°
  19. 75°
  20. 155°
  21. 75°
  22. 85°
  23. 150°
  24. 100°
  25. 15°
  26. 125°
  27. 120°
  28. 60°
  29. 140°
  30. 80°
  31. 10°
  32. 160°
  33. 30°
  34. 125°
  35. 60°
  36. 110°
  37. 105°
  38. 45°
  39. 80°
  40. 50°

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