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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 767 · 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.

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  1. 1.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  2. 2.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  3. 3.In triangle ABC, angle A = 58° and angle B = 96°. What is angle C (in degrees)?
  4. 4.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  6. 6.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  7. 7.Can a triangle have sides of 8 cm, 8 cm and 4 cm? (a) No (b) Yes
  8. 8.In an isosceles triangle, the two equal angles are 64° each. What is the third angle (in degrees)?
  9. 9.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 79°. What is the other one (in degrees)?
  10. 10.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  11. 11.In triangle ABC, angle A = 94° and angle B = 59°. What is angle C (in degrees)?
  12. 12.In an isosceles triangle, the two equal angles are 54° each. What is the third angle (in degrees)?
  13. 13.In an isosceles triangle, the two equal angles are 73° each. What is the third angle (in degrees)?
  14. 14.In an isosceles triangle, the two equal angles are 28° each. What is the third angle (in degrees)?
  15. 15.An exterior angle of a triangle is 107°. One of its two interior opposite angles is 60°. What is the other one (in degrees)?
  16. 16.In triangle ABC, angle A = 39° and angle B = 116°. What is angle C (in degrees)?
  17. 17.In triangle ABC, angle A = 43° and angle B = 88°. What is angle C (in degrees)?
  18. 18.In triangle ABC, angle A = 64° and angle B = 84°. What is angle C (in degrees)?
  19. 19.In an isosceles triangle, the two equal angles are 29° each. What is the third angle (in degrees)?
  20. 20.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  21. 21.Can a triangle have sides of 7 cm, 4 cm and 11 cm? (a) Yes (b) No
  22. 22.Can a triangle have sides of 6 cm, 8 cm and 12 cm? (a) No (b) Yes
  23. 23.The longest side of a right-angled triangle is 17 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  24. 24.An exterior angle of a triangle is 47°. One of its two interior opposite angles is 22°. What is the other one (in degrees)?
  25. 25.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  26. 26.In triangle ABC, angle A = 88° and angle B = 49°. What is angle C (in degrees)?
  27. 27.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  28. 28.The two interior opposite angles of a triangle are 72° and 72°. What is the exterior angle (in degrees)?
  29. 29.In an isosceles triangle, the two equal angles are 69° each. What is the third angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 78°. What is the third angle (in degrees)?
  31. 31.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  32. 32.In an isosceles triangle, the angle between the two equal sides is 46°. What is each of the other two angles (in degrees)?
  33. 33.The longest side of a right-angled triangle is 5 cm and one of the other sides is 4 cm. How long is the third side (in cm)?
  34. 34.Can a triangle have sides of 12 cm, 17 cm and 2 cm? (a) No (b) Yes
  35. 35.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 62°. What is the third angle (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 43° and 60°. What is the exterior angle (in degrees)?
  38. 38.Can a triangle have sides of 12 cm, 9 cm and 11 cm? (a) No (b) Yes
  39. 39.In triangle ABC, angle A = 47° and angle B = 30°. What is angle C (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 52°. What is the third angle (in degrees)?

Answer key

  1. 77
  2. 72
  3. 26
  4. 90
  5. 36
  6. 48
  7. Yes
  8. 52
  9. 30
  10. 36
  11. 27
  12. 72
  13. 34
  14. 124
  15. 47
  16. 25
  17. 49
  18. 32
  19. 122
  20. 84
  21. No
  22. Yes
  23. 15
  24. 25
  25. 72
  26. 43
  27. 25
  28. 144
  29. 42
  30. 12
  31. 18
  32. 67
  33. 3
  34. No
  35. 30
  36. 28
  37. 103
  38. Yes
  39. 103
  40. 38

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