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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 729 · 40 sums
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The method (Inside 180, outside the sum): Angle sum: ∠A + ∠B + ∠C = 180°. Exterior angle = sum of the two interior opposite angles. Right-angled triangle: longest side² = side² + side² (3, 4, 5 and 5, 12, 13 are famous sets). Sides can make a triangle only if the two shorter sides add up to more than the longest side.

NameDateTime takenScore ___ / 40
  1. 1.Can a triangle have sides of 13 cm, 12 cm and 4 cm? (a) No (b) Yes
  2. 2.In triangle ABC, angle A = 39° and angle B = 112°. What is angle C (in degrees)?
  3. 3.In a right-angled triangle, one of the other two angles is 68°. What is the third angle (in degrees)?
  4. 4.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  5. 5.The longest side of a right-angled triangle is 30 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  6. 6.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  7. 7.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  8. 8.Can a triangle have sides of 4 cm, 8 cm and 5 cm? (a) No (b) Yes
  9. 9.In a right-angled triangle, one of the other two angles is 31°. What is the third angle (in degrees)?
  10. 10.The longest side of a right-angled triangle is 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  11. 11.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  12. 12.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles (in degrees)?
  13. 13.In an isosceles triangle, the angle between the two equal sides is 82°. What is each of the other two angles (in degrees)?
  14. 14.In triangle ABC, angle A = 77° and angle B = 49°. What is angle C (in degrees)?
  15. 15.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  16. 16.In triangle ABC, angle A = 80° and angle B = 79°. What is angle C (in degrees)?
  17. 17.In an isosceles triangle, the angle between the two equal sides is 104°. What is each of the other two angles (in degrees)?
  18. 18.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  19. 19.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  20. 20.The longest side of a right-angled triangle is 25 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  21. 21.In triangle ABC, angle A = 84° and angle B = 49°. What is angle C (in degrees)?
  22. 22.In triangle ABC, angle A = 57° and angle B = 49°. What is angle C (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 78°. What is the third angle (in degrees)?
  24. 24.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  25. 25.An exterior angle of a triangle is 74°. One of its two interior opposite angles is 43°. What is the other one (in degrees)?
  26. 26.The two interior opposite angles of a triangle are 38° and 59°. What is the exterior angle (in degrees)?
  27. 27.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 92°. What is each of the other two angles (in degrees)?
  29. 29.In triangle ABC, angle A = 66° and angle B = 85°. What is angle C (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  31. 31.Can a triangle have sides of 11 cm, 2 cm and 18 cm? (a) No (b) Yes
  32. 32.In triangle ABC, angle A = 48° and angle B = 37°. What is angle C (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 43°. What is the third angle (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 73° and 73°. What is the exterior angle (in degrees)?
  35. 35.In an isosceles triangle, the angle between the two equal sides is 112°. What is each of the other two angles (in degrees)?
  36. 36.An exterior angle of a triangle is 123°. One of its two interior opposite angles is 56°. What is the other one (in degrees)?
  37. 37.An exterior angle of a triangle is 68°. One of its two interior opposite angles is 41°. What is the other one (in degrees)?
  38. 38.In a right-angled triangle, one of the other two angles is 18°. What is the third angle (in degrees)?
  39. 39.Can a triangle have sides of 7 cm, 11 cm and 22 cm? (a) Yes (b) No
  40. 40.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?

Answer key

  1. Yes
  2. 29
  3. 22
  4. 25
  5. 18
  6. 45
  7. 17
  8. Yes
  9. 59
  10. 24
  11. 40
  12. 20
  13. 49
  14. 54
  15. 40
  16. 21
  17. 38
  18. 90
  19. 70
  20. 7
  21. 47
  22. 74
  23. 12
  24. 100
  25. 31
  26. 97
  27. 62
  28. 44
  29. 29
  30. 69
  31. No
  32. 95
  33. 47
  34. 146
  35. 34
  36. 67
  37. 27
  38. 72
  39. No
  40. 64

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