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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 4 · 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 angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 130° (d) 40°
  2. 2.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
  4. 4.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  5. 5.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
  6. 6.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 120° (c) 60° (d) 61°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 50° (d) 80°
  8. 8.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
  11. 11.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 210° (c) 150° (d) 105°
  12. 12.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 35°
  13. 13.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 65° (b) 110° (c) 115° (d) 135°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 90° (d) 135°
  15. 15.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 150° (b) 75° (c) 135° (d) 105°
  16. 16.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 165° (d) 16°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 50° (d) 130°
  18. 18.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°
  19. 19.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) 50° (c) 320° (d) 40°
  20. 20.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 260° (b) 100° (c) 160° (d) 80°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 20° (d) 70°
  22. 22.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  23. 23.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 46° (c) 135° (d) 225°
  24. 24.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 70° (d) 100°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 11° (c) 20° (d) 170°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 120° (d) 30°
  27. 27.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
  28. 28.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 125° (d) 105°
  29. 29.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 115° (c) 230° (d) 130°
  30. 30.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 105° (d) 120°
  31. 31.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 95° (b) 135° (c) 85° (d) 130°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
  33. 33.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 65° (b) 110° (c) 115° (d) 135°
  34. 34.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 275° (c) 85° (d) 95°
  35. 35.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 130° (c) 50° (d) 230°
  36. 36.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 70° (b) 110° (c) 100° (d) 150°
  37. 37.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) 300° (c) 120° (d) 30°
  38. 38.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 80° (c) 160° (d) 100°
  39. 39.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 90° (b) 120° (c) 150° (d) 60°
  40. 40.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 135° (d) 160°

Answer key

  1. 65°
  2. 110°
  3. 55°
  4. 30°
  5. 20°
  6. 60°
  7. 40°
  8. 125°
  9. 85°
  10. 95°
  11. 30°
  12. 35°
  13. 65°
  14. 135°
  15. 105°
  16. 15°
  17. 130°
  18. 120°
  19. 140°
  20. 80°
  21. 55°
  22. 70°
  23. 45°
  24. 110°
  25. 10°
  26. 30°
  27. 140°
  28. 75°
  29. 50°
  30. 105°
  31. 85°
  32. 35°
  33. 115°
  34. 95°
  35. 50°
  36. 70°
  37. 120°
  38. 80°
  39. 60°
  40. 45°

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