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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 822 · 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.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  2. 2.An exterior angle of a triangle is 73°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  3. 3.The two interior opposite angles of a triangle are 21° and 30°. What is the exterior angle (in degrees)?
  4. 4.In triangle ABC, angle A = 88° and angle B = 66°. What is angle C (in degrees)?
  5. 5.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  6. 6.The longest side of a right-angled triangle is 10 cm and one of the other sides is 6 cm. How long is the third side (in cm)?
  7. 7.Can a triangle have sides of 2 cm, 6 cm and 5 cm? (a) No (b) Yes
  8. 8.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 62°. What is the third angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  12. 12.In triangle ABC, angle A = 84° and angle B = 62°. What is angle C (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 76°. What is the third angle (in degrees)?
  14. 14.An exterior angle of a triangle is 71°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  15. 15.An exterior angle of a triangle is 108°. One of its two interior opposite angles is 41°. What is the other one (in degrees)?
  16. 16.In triangle ABC, angle A = 35° and angle B = 122°. What is angle C (in degrees)?
  17. 17.In a right-angled triangle, one of the other two angles is 71°. What is the third angle (in degrees)?
  18. 18.An exterior angle of a triangle is 124°. One of its two interior opposite angles is 61°. What is the other one (in degrees)?
  19. 19.In an isosceles triangle, the two equal angles are 51° each. What is the third angle (in degrees)?
  20. 20.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  21. 21.In an isosceles triangle, the two equal angles are 52° each. What is the third angle (in degrees)?
  22. 22.In triangle ABC, angle A = 30° and angle B = 114°. What is angle C (in degrees)?
  23. 23.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  24. 24.Can a triangle have sides of 14 cm, 11 cm and 2 cm? (a) Yes (b) No
  25. 25.In a right-angled triangle, one of the other two angles is 45°. What is the third angle (in degrees)?
  26. 26.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)?
  27. 27.In an isosceles triangle, the two equal angles are 56° each. What is the third angle (in degrees)?
  28. 28.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  29. 29.The two interior opposite angles of a triangle are 60° and 39°. What is the exterior angle (in degrees)?
  30. 30.The two interior opposite angles of a triangle are 76° and 50°. What is the exterior angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 41°. What is the third angle (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 24° and 65°. What is the exterior angle (in degrees)?
  33. 33.The two interior opposite angles of a triangle are 58° and 72°. What is the exterior angle (in degrees)?
  34. 34.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  35. 35.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles (in degrees)?
  36. 36.An exterior angle of a triangle is 99°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 73° and 53°. What is the exterior angle (in degrees)?
  38. 38.Can a triangle have sides of 19 cm, 6 cm and 8 cm? (a) No (b) Yes
  39. 39.The two interior opposite angles of a triangle are 31° and 46°. What is the exterior angle (in degrees)?
  40. 40.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles (in degrees)?

Answer key

  1. 17
  2. 36
  3. 51
  4. 26
  5. 25
  6. 8
  7. Yes
  8. 84
  9. 28
  10. 64
  11. 34
  12. 34
  13. 14
  14. 40
  15. 67
  16. 23
  17. 19
  18. 63
  19. 78
  20. 90
  21. 76
  22. 36
  23. 40
  24. No
  25. 45
  26. 15
  27. 68
  28. 90
  29. 99
  30. 126
  31. 49
  32. 89
  33. 130
  34. 120
  35. 35
  36. 22
  37. 126
  38. No
  39. 77
  40. 15

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