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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 376 · 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 straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 80° (c) 260° (d) 100°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 115° (d) 295°
  4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
  5. 5.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 55° (d) 125°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 40° (d) 50°
  7. 7.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 260° (c) 80° (d) 100°
  8. 8.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 35° (c) 215° (d) 145°
  9. 9.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 115° (c) 65° (d) 135°
  10. 10.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
  11. 11.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 125° (b) 165° (c) 15° (d) 70°
  12. 12.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 200° (c) 160° (d) 21°
  13. 13.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 95° (c) 130° (d) 85°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 60° (d) 30°
  15. 15.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 60°
  16. 16.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 155° (c) 25° (d) 110°
  17. 17.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 155° (d) 65°
  18. 18.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 125° (b) 140° (c) 95° (d) 85°
  19. 19.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 115° (c) 95° (d) 160°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 85° (c) 10° (d) 190°
  21. 21.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) 310° (d) 155°
  22. 22.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 70°
  23. 23.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 85° (d) 120°
  24. 24.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  25. 25.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 115° (c) 140° (d) 105°
  26. 26.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 145° (c) 70° (d) 105°
  27. 27.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) 80° (d) 50°
  28. 28.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 320° (d) 50°
  29. 29.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 135° (c) 225° (d) 45°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 145° (d) 290°
  31. 31.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 130° (d) 115°
  32. 32.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 55° (b) 125° (c) 110° (d) 235°
  33. 33.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 85° (b) 125° (c) 140° (d) 95°
  34. 34.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 115° (b) 35° (c) 145° (d) 100°
  35. 35.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 145° (d) 35°
  36. 36.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 150° (b) 55° (c) 155° (d) 30°
  37. 37.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 100° (d) 130°
  38. 38.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  39. 39.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  40. 40.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 15° (b) 165° (c) 100° (d) 95°

Answer key

  1. 80°
  2. 65°
  3. 115°
  4. 100°
  5. 125°
  6. 40°
  7. 100°
  8. 35°
  9. 65°
  10. 85°
  11. 15°
  12. 20°
  13. 95°
  14. 30°
  15. 120°
  16. 25°
  17. 65°
  18. 95°
  19. 95°
  20. 95°
  21. 155°
  22. 70°
  23. 95°
  24. 120°
  25. 40°
  26. 70°
  27. 50°
  28. 140°
  29. 135°
  30. 145°
  31. 115°
  32. 55°
  33. 85°
  34. 35°
  35. 110°
  36. 30°
  37. 80°
  38. 130°
  39. 20°
  40. 15°

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