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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 960 · 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 67°. What is the third angle (in degrees)?
  2. 2.The two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 142°. What is each of the other two angles (in degrees)?
  4. 4.The two interior opposite angles of a triangle are 52° and 60°. What is the exterior angle (in degrees)?
  5. 5.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  6. 6.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  7. 7.Can a triangle have sides of 13 cm, 7 cm and 12 cm? (a) No (b) Yes
  8. 8.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  9. 9.The two interior opposite angles of a triangle are 76° and 72°. What is the exterior angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  11. 11.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  12. 12.An exterior angle of a triangle is 56°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 20°. What is the third angle (in degrees)?
  14. 14.An exterior angle of a triangle is 82°. One of its two interior opposite angles is 48°. What is the other one (in degrees)?
  15. 15.The two shorter sides of a right-angled triangle are 12 cm and 16 cm. How long is the longest side (in cm)?
  16. 16.The two interior opposite angles of a triangle are 65° and 66°. What is the exterior angle (in degrees)?
  17. 17.The two interior opposite angles of a triangle are 30° and 34°. What is the exterior angle (in degrees)?
  18. 18.Can a triangle have sides of 11 cm, 12 cm and 3 cm? (a) No (b) Yes
  19. 19.In triangle ABC, angle A = 76° and angle B = 60°. What is angle C (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 9 cm, 12 cm and 7 cm? (a) Yes (b) No
  22. 22.In a right-angled triangle, one of the other two angles is 36°. What is the third angle (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 11°. What is the third angle (in degrees)?
  24. 24.The two interior opposite angles of a triangle are 27° and 45°. What is the exterior angle (in degrees)?
  25. 25.In an isosceles triangle, the two equal angles are 49° each. What is the third angle (in degrees)?
  26. 26.In an isosceles triangle, the two equal angles are 25° each. What is the third angle (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 79° each. What is the third angle (in degrees)?
  28. 28.An exterior angle of a triangle is 76°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  29. 29.In an isosceles triangle, the angle between the two equal sides is 88°. What is each of the other two angles (in degrees)?
  30. 30.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)?
  31. 31.The two interior opposite angles of a triangle are 20° and 78°. What is the exterior angle (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 48° and 54°. What is the exterior angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 144°. What is each of the other two angles (in degrees)?
  35. 35.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)?
  36. 36.In triangle ABC, angle A = 42° and angle B = 104°. What is angle C (in degrees)?
  37. 37.Can a triangle have sides of 10 cm, 10 cm and 3 cm? (a) Yes (b) No
  38. 38.The two interior opposite angles of a triangle are 76° and 25°. What is the exterior angle (in degrees)?
  39. 39.Can a triangle have sides of 11 cm, 20 cm and 9 cm? (a) Yes (b) No
  40. 40.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)?

Answer key

  1. 23
  2. 26
  3. 19
  4. 112
  5. 68
  6. 12
  7. Yes
  8. 54
  9. 148
  10. 66
  11. 45
  12. 30
  13. 70
  14. 34
  15. 20
  16. 131
  17. 64
  18. Yes
  19. 44
  20. 84
  21. Yes
  22. 54
  23. 79
  24. 72
  25. 82
  26. 130
  27. 22
  28. 21
  29. 46
  30. 24
  31. 98
  32. 102
  33. 40
  34. 18
  35. 15
  36. 34
  37. Yes
  38. 101
  39. No
  40. 8

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