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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 944 · 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 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 260° (d) 80°
  2. 2.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 60° (d) 160°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
  4. 4.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 35° (b) 160° (c) 145° (d) 55°
  5. 5.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 110° (d) 45°
  6. 6.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 250° (c) 70° (d) 110°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
  8. 8.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 100° (b) 130° (c) 260° (d) 80°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 20° (c) 140° (d) 320°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
  11. 11.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 110°
  12. 12.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 70° (b) 130° (c) 160° (d) 20°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 80° (d) 160°
  14. 14.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 46° (d) 225°
  15. 15.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 130° (c) 50° (d) 140°
  16. 16.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) 11° (d) 10°
  17. 17.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 75° (c) 105° (d) 160°
  18. 18.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) 85° (c) 275° (d) 95°
  19. 19.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) 150° (d) 75°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 95° (c) 190° (d) 85°
  21. 21.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 335° (d) 65°
  22. 22.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 155° (b) 160° (c) 45° (d) 135°
  23. 23.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 55° (d) 125°
  24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 25° (d) 65°
  25. 25.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 35° (c) 125° (d) 145°
  26. 26.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 130° (c) 55° (d) 125°
  27. 27.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) 136° (c) 45° (d) 135°
  28. 28.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 15° (b) 65° (c) 165° (d) 130°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 30° (d) 150°
  30. 30.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  31. 31.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 140° (c) 115° (d) 105°
  32. 32.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 120° (c) 100° (d) 140°
  33. 33.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 90° (d) 135°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 145° (d) 35°
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 115° (d) 50°
  36. 36.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 160° (b) 125° (c) 145° (d) 55°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 80° (d) 260°
  39. 39.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
  40. 40.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°

Answer key

  1. 100°
  2. 120°
  3. 45°
  4. 35°
  5. 135°
  6. 110°
  7. 85°
  8. 80°
  9. 160°
  10. 20°
  11. 80°
  12. 20°
  13. 80°
  14. 45°
  15. 130°
  16. 10°
  17. 105°
  18. 95°
  19. 75°
  20. 95°
  21. 155°
  22. 135°
  23. 70°
  24. 130°
  25. 145°
  26. 55°
  27. 135°
  28. 15°
  29. 15°
  30. 135°
  31. 65°
  32. 140°
  33. 90°
  34. 145°
  35. 50°
  36. 125°
  37. 65°
  38. 130°
  39. 85°
  40. 15°

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