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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 219 · 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 angles of a triangle are 30° and 85°. What is the third angle? (a) 65° (b) 95° (c) 150° (d) 115°
  2. 2.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 75° (c) 160° (d) 105°
  3. 3.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
  4. 4.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
  5. 5.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 100°
  6. 6.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
  7. 7.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 125° (b) 100° (c) 155° (d) 80°
  8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  9. 9.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 130° (b) 150° (c) 30° (d) 80°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
  11. 11.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 100° (c) 145° (d) 80°
  12. 12.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 160° (c) 35° (d) 165°
  13. 13.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 150° (c) 30° (d) 50°
  14. 14.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 115° (b) 155° (c) 90° (d) 25°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
  16. 16.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 100° (b) 165° (c) 15° (d) 95°
  17. 17.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 130° (c) 115° (d) 65°
  18. 18.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 105° (b) 120° (c) 60° (d) 135°
  19. 19.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 110° (c) 145° (d) 290°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 160° (c) 21° (d) 20°
  21. 21.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 115° (c) 65° (d) 145°
  22. 22.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
  23. 23.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 130° (b) 145° (c) 95° (d) 85°
  24. 24.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 190° (c) 85° (d) 10°
  26. 26.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 65° (d) 115°
  27. 27.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 110° (d) 70°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 25° (d) 35°
  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) 320° (b) 50° (c) 140° (d) 40°
  30. 30.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 150° (b) 210° (c) 60° (d) 30°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 20° (d) 140°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
  33. 33.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 35° (c) 145° (d) 36°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 165° (d) 16°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 110° (c) 55° (d) 125°
  36. 36.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  38. 38.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 85° (d) 110°
  39. 39.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 200° (b) 20° (c) 160° (d) 40°
  40. 40.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 250° (d) 110°

Answer key

  1. 65°
  2. 105°
  3. 135°
  4. 90°
  5. 100°
  6. 30°
  7. 100°
  8. 80°
  9. 30°
  10. 60°
  11. 100°
  12. 15°
  13. 30°
  14. 25°
  15. 70°
  16. 15°
  17. 115°
  18. 60°
  19. 110°
  20. 20°
  21. 65°
  22. 130°
  23. 95°
  24. 50°
  25. 95°
  26. 65°
  27. 70°
  28. 25°
  29. 140°
  30. 30°
  31. 20°
  32. 65°
  33. 35°
  34. 15°
  35. 55°
  36. 20°
  37. 35°
  38. 15°
  39. 20°
  40. 110°

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