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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 359 · 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 40° and 25°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 155°
  2. 2.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°
  3. 3.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 130° (d) 230°
  4. 4.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 30° (b) 60° (c) 210° (d) 150°
  5. 5.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 130° (b) 70° (c) 20° (d) 160°
  6. 6.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°
  7. 7.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 105° (c) 140° (d) 115°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
  9. 9.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 105° (c) 80° (d) 100°
  10. 10.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 80° (b) 100° (c) 115° (d) 145°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 15° (d) 30°
  12. 12.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 85° (d) 145°
  13. 13.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 50° (d) 115°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 30° (c) 210° (d) 75°
  15. 15.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) 190° (c) 10° (d) 11°
  16. 16.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 90° (b) 50° (c) 130° (d) 140°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 50° (d) 130°
  18. 18.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 45° (b) 20° (c) 160° (d) 155°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  20. 20.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 150° (b) 45° (c) 75° (d) 135°
  21. 21.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°
  22. 22.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 70° (d) 20°
  23. 23.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 105° (c) 75° (d) 76°
  25. 25.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°
  26. 26.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 155° (c) 95° (d) 110°
  27. 27.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
  28. 28.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 100° (d) 140°
  29. 29.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 90° (c) 91° (d) 135°
  30. 30.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 50° (d) 130°
  31. 31.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 40° (c) 140° (d) 105°
  32. 32.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 125° (d) 155°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 170° (d) 10°
  35. 35.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 125° (b) 60° (c) 115° (d) 120°
  36. 36.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 145° (b) 120° (c) 60° (d) 95°
  37. 37.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) 170° (d) 86°
  38. 38.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 30° (c) 300° (d) 60°
  39. 39.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 85° (d) 140°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 20° (d) 70°

Answer key

  1. 115°
  2. 15°
  3. 130°
  4. 150°
  5. 20°
  6. 95°
  7. 40°
  8. 75°
  9. 80°
  10. 80°
  11. 15°
  12. 85°
  13. 50°
  14. 105°
  15. 10°
  16. 50°
  17. 65°
  18. 20°
  19. 140°
  20. 45°
  21. 30°
  22. 110°
  23. 60°
  24. 75°
  25. 135°
  26. 85°
  27. 20°
  28. 100°
  29. 90°
  30. 130°
  31. 140°
  32. 80°
  33. 160°
  34. 10°
  35. 60°
  36. 60°
  37. 85°
  38. 120°
  39. 85°
  40. 80°

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