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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 144 · 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 60° and 70°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 130° (d) 110°
  2. 2.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) 65° (d) 130°
  3. 3.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 110° (b) 105° (c) 35° (d) 145°
  4. 4.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 135° (c) 70° (d) 110°
  5. 5.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°
  6. 6.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 100° (c) 20° (d) 200°
  7. 7.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
  8. 8.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 290° (c) 145° (d) 70°
  9. 9.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 150° (c) 25° (d) 55°
  10. 10.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
  11. 11.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
  12. 12.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 25° (d) 115°
  13. 13.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 130° (d) 60°
  14. 14.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 115°
  15. 15.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 145° (d) 215°
  16. 16.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 75° (d) 45°
  17. 17.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 45° (c) 135° (d) 46°
  18. 18.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 115° (c) 245° (d) 66°
  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) 40° (b) 50° (c) 320° (d) 140°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 130° (d) 25°
  21. 21.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 91° (b) 270° (c) 90° (d) 135°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 35° (c) 145° (d) 290°
  23. 23.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 100° (c) 80° (d) 280°
  24. 24.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 75° (d) 105°
  26. 26.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 340° (c) 20° (d) 70°
  27. 27.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 85° (d) 95°
  28. 28.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
  29. 29.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 75°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 160°
  31. 31.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
  34. 34.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 145° (c) 75° (d) 105°
  35. 35.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 55° (c) 125° (d) 150°
  36. 36.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) 35° (d) 50°
  37. 37.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) 135° (c) 136° (d) 45°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 55°
  39. 39.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 260° (d) 80°

Answer key

  1. 130°
  2. 65°
  3. 35°
  4. 70°
  5. 10°
  6. 20°
  7. 10°
  8. 70°
  9. 25°
  10. 30°
  11. 70°
  12. 115°
  13. 120°
  14. 115°
  15. 35°
  16. 135°
  17. 45°
  18. 65°
  19. 140°
  20. 155°
  21. 90°
  22. 145°
  23. 100°
  24. 30°
  25. 75°
  26. 160°
  27. 85°
  28. 10°
  29. 105°
  30. 10°
  31. 65°
  32. 75°
  33. 85°
  34. 75°
  35. 125°
  36. 25°
  37. 135°
  38. 45°
  39. 100°
  40. 130°

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