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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 506 · 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. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
  2. 2.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  3. 3.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 85° (d) 95°
  4. 4.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 55° (d) 125°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 15° (c) 16° (d) 30°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
  7. 7.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 45° (c) 135° (d) 160°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 61° (c) 120° (d) 59°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  10. 10.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
  11. 11.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 70° (c) 100° (d) 150°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 270°
  13. 13.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 135° (d) 45°
  14. 14.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) 145° (c) 215° (d) 35°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 30° (c) 31° (d) 60°
  16. 16.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 135° (c) 45° (d) 90°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 55°
  18. 18.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 90° (c) 15° (d) 165°
  19. 19.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 135° (d) 45°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  21. 21.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 140° (b) 320° (c) 160° (d) 40°
  22. 22.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 11° (c) 10° (d) 190°
  23. 23.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
  24. 24.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 30° (d) 60°
  25. 25.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 15° (c) 195° (d) 16°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 130° (d) 65°
  27. 27.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 210° (d) 150°
  28. 28.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 115° (d) 65°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
  30. 30.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 275° (d) 5°
  31. 31.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 20° (d) 160°
  32. 32.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 160° (d) 100°
  34. 34.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 125° (d) 90°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°
  36. 36.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 65° (b) 140° (c) 115° (d) 105°
  37. 37.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 115°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
  39. 39.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 155° (b) 15° (c) 165° (d) 40°
  40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°

Answer key

  1. 155°
  2. 80°
  3. 95°
  4. 125°
  5. 15°
  6. 10°
  7. 135°
  8. 60°
  9. 50°
  10. 100°
  11. 70°
  12. 135°
  13. 135°
  14. 35°
  15. 30°
  16. 45°
  17. 45°
  18. 15°
  19. 135°
  20. 70°
  21. 140°
  22. 10°
  23. 50°
  24. 120°
  25. 15°
  26. 65°
  27. 30°
  28. 115°
  29. 60°
  30. 95°
  31. 20°
  32. 65°
  33. 80°
  34. 125°
  35. 25°
  36. 65°
  37. 95°
  38. 10°
  39. 15°
  40. 130°

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