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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 995 · 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.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 110° (d) 40°
  2. 2.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 45° (b) 120° (c) 135° (d) 105°
  3. 3.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 270° (c) 130° (d) 90°
  4. 4.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 55° (d) 325°
  5. 5.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 75° (b) 105° (c) 155° (d) 100°
  6. 6.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) 130° (d) 65°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 110° (d) 220°
  9. 9.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 90° (b) 115° (c) 155° (d) 270°
  10. 10.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 115° (b) 90° (c) 65° (d) 155°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
  12. 12.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 95° (d) 135°
  13. 13.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 90°
  14. 14.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°
  15. 15.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
  16. 16.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 85° (c) 110° (d) 95°
  17. 17.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 125° (c) 55° (d) 130°
  18. 18.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°
  19. 19.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 105° (d) 285°
  20. 20.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 125° (d) 55°
  21. 21.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) 36° (d) 145°
  22. 22.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) 85° (c) 265° (d) 86°
  23. 23.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 115° (b) 75° (c) 140° (d) 105°
  24. 24.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  25. 25.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 70° (b) 110° (c) 150° (d) 140°
  26. 26.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) 85° (d) 190°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 46° (d) 55°
  28. 28.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 155° (c) 50° (d) 75°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 80° (d) 20°
  31. 31.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 115° (d) 105°
  32. 32.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 80° (c) 100° (d) 81°
  33. 33.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 55° (c) 125° (d) 235°
  34. 34.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 35° (c) 145° (d) 100°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 30° (c) 165° (d) 15°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
  37. 37.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 115° (b) 60° (c) 120° (d) 125°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
  39. 39.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 50° (c) 30° (d) 150°
  40. 40.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 115° (d) 25°

Answer key

  1. 40°
  2. 135°
  3. 90°
  4. 145°
  5. 75°
  6. 65°
  7. 25°
  8. 110°
  9. 90°
  10. 65°
  11. 55°
  12. 85°
  13. 30°
  14. 160°
  15. 110°
  16. 85°
  17. 55°
  18. 35°
  19. 105°
  20. 125°
  21. 35°
  22. 85°
  23. 75°
  24. 100°
  25. 110°
  26. 95°
  27. 45°
  28. 50°
  29. 135°
  30. 80°
  31. 105°
  32. 80°
  33. 125°
  34. 145°
  35. 15°
  36. 60°
  37. 60°
  38. 50°
  39. 150°
  40. 50°

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