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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 755 · 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 95°. What is the exterior angle at the third corner? (a) 45° (b) 140° (c) 85° (d) 135°
  2. 2.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
  3. 3.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 95° (c) 85° (d) 135°
  4. 4.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 160° (c) 55° (d) 145°
  5. 5.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 50° (c) 130° (d) 155°
  6. 6.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
  7. 7.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 75° (d) 105°
  8. 8.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 90° (b) 115° (c) 270° (d) 155°
  9. 9.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 115° (c) 165° (d) 80°
  10. 10.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 50° (d) 10°
  11. 11.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 280° (c) 80° (d) 140°
  12. 12.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 80° (d) 100°
  13. 13.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 145°
  14. 14.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 85° (d) 10°
  15. 15.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 250° (d) 70°
  16. 16.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 65° (d) 115°
  17. 17.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 155° (c) 25° (d) 100°
  18. 18.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 25° (d) 115°
  19. 19.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°
  20. 20.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 35° (b) 160° (c) 55° (d) 145°
  21. 21.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 100° (c) 145° (d) 80°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 170° (c) 20° (d) 10°
  23. 23.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 210° (c) 150° (d) 60°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 20° (d) 160°
  25. 25.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 75° (b) 35° (c) 145° (d) 140°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 40°
  27. 27.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 50° (d) 80°
  28. 28.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°
  29. 29.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) 80° (c) 100° (d) 280°
  30. 30.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 145° (c) 55° (d) 160°
  31. 31.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 110° (d) 95°
  32. 32.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 50° (c) 110° (d) 130°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 55° (d) 45°
  34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 40° (d) 140°
  36. 36.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 20° (d) 160°
  37. 37.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) 10° (c) 190° (d) 170°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  39. 39.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°
  40. 40.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 65° (c) 115° (d) 125°

Answer key

  1. 135°
  2. 130°
  3. 95°
  4. 55°
  5. 50°
  6. 40°
  7. 105°
  8. 90°
  9. 15°
  10. 10°
  11. 100°
  12. 80°
  13. 95°
  14. 10°
  15. 110°
  16. 115°
  17. 25°
  18. 50°
  19. 135°
  20. 35°
  21. 100°
  22. 10°
  23. 30°
  24. 10°
  25. 35°
  26. 40°
  27. 80°
  28. 85°
  29. 100°
  30. 125°
  31. 95°
  32. 130°
  33. 45°
  34. 120°
  35. 70°
  36. 160°
  37. 10°
  38. 75°
  39. 135°
  40. 65°

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