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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 856 · 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 45° and 85°. What is the exterior angle at the third corner? (a) 130° (b) 135° (c) 50° (d) 95°
  2. 2.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°
  3. 3.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 70° (c) 110° (d) 135°
  4. 4.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 285° (c) 105° (d) 75°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 270°
  6. 6.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 60°
  7. 7.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 140° (c) 105° (d) 145°
  8. 8.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 60° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
  10. 10.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 160° (b) 115° (c) 95° (d) 85°
  11. 11.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) 11° (c) 190° (d) 10°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 86° (d) 170°
  13. 13.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 65°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  15. 15.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 45° (d) 135°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 110° (c) 40° (d) 70°
  17. 17.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 50° (d) 160°
  18. 18.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 115° (c) 35° (d) 145°
  19. 19.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 160° (d) 125°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 100° (d) 80°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 26° (c) 25° (d) 155°
  22. 22.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 160° (b) 75° (c) 105° (d) 125°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 310° (c) 25° (d) 155°
  24. 24.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 140° (d) 75°
  25. 25.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 120° (b) 10° (c) 170° (d) 70°
  26. 26.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 80° (c) 45° (d) 145°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 70°
  28. 28.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 35°
  29. 29.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 270° (c) 90° (d) 145°
  30. 30.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 155° (c) 270° (d) 115°
  31. 31.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
  32. 32.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 130° (b) 85° (c) 95° (d) 145°
  33. 33.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
  34. 34.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°
  35. 35.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 110° (c) 250° (d) 70°
  36. 36.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 70° (d) 140°
  37. 37.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°
  38. 38.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 65° (b) 10° (c) 170° (d) 125°
  39. 39.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) 55° (c) 35° (d) 145°
  40. 40.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 55° (c) 105° (d) 125°

Answer key

  1. 130°
  2. 130°
  3. 110°
  4. 105°
  5. 135°
  6. 60°
  7. 105°
  8. 60°
  9. 70°
  10. 95°
  11. 10°
  12. 85°
  13. 130°
  14. 15°
  15. 45°
  16. 110°
  17. 50°
  18. 35°
  19. 55°
  20. 80°
  21. 25°
  22. 105°
  23. 155°
  24. 75°
  25. 10°
  26. 45°
  27. 60°
  28. 35°
  29. 90°
  30. 90°
  31. 85°
  32. 95°
  33. 40°
  34. 10°
  35. 70°
  36. 70°
  37. 45°
  38. 10°
  39. 145°
  40. 125°

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