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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 191 · 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 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 230° (d) 50°
  2. 2.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 55° (d) 35°
  3. 3.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 140° (d) 50°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 160°
  5. 5.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) 165° (d) 15°
  6. 6.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 35° (c) 70° (d) 145°
  7. 7.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 140° (c) 280° (d) 100°
  8. 8.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  9. 9.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 100° (c) 80° (d) 150°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 10° (d) 80°
  11. 11.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 65° (d) 115°
  12. 12.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 20° (b) 160° (c) 60° (d) 140°
  13. 13.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 35° (c) 55° (d) 145°
  14. 14.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
  15. 15.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 120° (b) 55° (c) 125° (d) 115°
  16. 16.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 35°
  17. 17.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  19. 19.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) 130° (d) 155°
  20. 20.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 40° (c) 220° (d) 140°
  21. 21.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 115° (b) 95° (c) 150° (d) 65°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
  23. 23.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 115° (d) 150°
  24. 24.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 65° (d) 140°
  25. 25.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 40° (c) 135° (d) 140°
  26. 26.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 36° (c) 35° (d) 215°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
  28. 28.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 55° (b) 125° (c) 155° (d) 80°
  29. 29.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 95° (b) 145° (c) 60° (d) 120°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 110° (d) 35°
  31. 31.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 40° (c) 50° (d) 310°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 45° (c) 135° (d) 46°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°
  34. 34.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 135° (d) 95°
  35. 35.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 95° (d) 130°
  36. 36.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
  37. 37.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 150° (c) 35° (d) 145°
  38. 38.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 140° (c) 45° (d) 135°
  39. 39.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 20° (d) 70°
  40. 40.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 135° (d) 110°

Answer key

  1. 50°
  2. 125°
  3. 140°
  4. 10°
  5. 15°
  6. 145°
  7. 100°
  8. 70°
  9. 80°
  10. 50°
  11. 115°
  12. 20°
  13. 145°
  14. 90°
  15. 55°
  16. 145°
  17. 85°
  18. 70°
  19. 155°
  20. 40°
  21. 65°
  22. 125°
  23. 65°
  24. 65°
  25. 140°
  26. 35°
  27. 35°
  28. 55°
  29. 60°
  30. 145°
  31. 130°
  32. 45°
  33. 110°
  34. 95°
  35. 95°
  36. 140°
  37. 35°
  38. 45°
  39. 160°
  40. 135°

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