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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 635 · 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 an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles (in degrees)?
  2. 2.In an isosceles triangle, the angle between the two equal sides is 128°. What is each of the other two angles (in degrees)?
  3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle (in degrees)?
  4. 4.An exterior angle of a triangle is 144°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  5. 5.In an isosceles triangle, the two equal angles are 42° each. What is the third angle (in degrees)?
  6. 6.The two interior opposite angles of a triangle are 54° and 42°. What is the exterior angle (in degrees)?
  7. 7.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  8. 8.The two interior opposite angles of a triangle are 60° and 71°. What is the exterior angle (in degrees)?
  9. 9.Can a triangle have sides of 9 cm, 26 cm and 12 cm? (a) Yes (b) No
  10. 10.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  11. 11.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  12. 12.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  13. 13.In triangle ABC, angle A = 91° and angle B = 60°. What is angle C (in degrees)?
  14. 14.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  15. 15.The two interior opposite angles of a triangle are 55° and 34°. What is the exterior angle (in degrees)?
  16. 16.In triangle ABC, angle A = 22° and angle B = 43°. What is angle C (in degrees)?
  17. 17.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  18. 18.The angles of a triangle are in the ratio 4 : 5 : 6. 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.In an isosceles triangle, the angle between the two equal sides is 102°. What is each of the other two angles (in degrees)?
  21. 21.In a right-angled triangle, one of the other two angles is 63°. What is the third angle (in degrees)?
  22. 22.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)?
  23. 23.The longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  24. 24.The two shorter sides of a right-angled triangle are 12 cm and 16 cm. How long is the longest side (in cm)?
  25. 25.In an isosceles triangle, the two equal angles are 34° each. What is the third angle (in degrees)?
  26. 26.The two interior opposite angles of a triangle are 63° and 36°. What is the exterior angle (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 28° each. What is the third angle (in degrees)?
  28. 28.In triangle ABC, angle A = 91° and angle B = 31°. What is angle C (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 16°. What is the third angle (in degrees)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 114°. What is each of the other two angles (in degrees)?
  31. 31.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  32. 32.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  33. 33.Can a triangle have sides of 14 cm, 11 cm and 5 cm? (a) Yes (b) No
  34. 34.In triangle ABC, angle A = 96° and angle B = 34°. What is angle C (in degrees)?
  35. 35.The two interior opposite angles of a triangle are 22° and 57°. What is the exterior angle (in degrees)?
  36. 36.Can a triangle have sides of 17 cm, 6 cm and 6 cm? (a) Yes (b) No
  37. 37.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)?
  38. 38.In a right-angled triangle, one of the other two angles is 38°. What is the third angle (in degrees)?
  39. 39.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 47°. What is the other one (in degrees)?
  40. 40.An exterior angle of a triangle is 133°. One of its two interior opposite angles is 56°. What is the other one (in degrees)?

Answer key

  1. 15
  2. 26
  3. 120
  4. 72
  5. 96
  6. 96
  7. 13
  8. 131
  9. No
  10. 40
  11. 25
  12. 51
  13. 29
  14. 48
  15. 89
  16. 115
  17. 100
  18. 72
  19. 70
  20. 39
  21. 27
  22. 15
  23. 36
  24. 20
  25. 112
  26. 99
  27. 124
  28. 58
  29. 74
  30. 33
  31. 80
  32. 20
  33. Yes
  34. 50
  35. 79
  36. No
  37. 24
  38. 52
  39. 34
  40. 77

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