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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 452 · 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 156°. What is each of the other two angles (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  3. 3.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 35°. What is the other one (in degrees)?
  4. 4.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 52°. What is the other one (in degrees)?
  5. 5.The two shorter sides of a right-angled triangle are 16 cm and 12 cm. How long is the longest side (in cm)?
  6. 6.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  7. 7.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  8. 8.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 54°. What is each of the other two angles (in degrees)?
  10. 10.The two interior opposite angles of a triangle are 23° and 44°. What is the exterior angle (in degrees)?
  11. 11.An exterior angle of a triangle is 58°. One of its two interior opposite angles is 35°. What is the other one (in degrees)?
  12. 12.In triangle ABC, angle A = 55° and angle B = 103°. What is angle C (in degrees)?
  13. 13.In triangle ABC, angle A = 34° and angle B = 113°. What is angle C (in degrees)?
  14. 14.An exterior angle of a triangle is 93°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  15. 15.The two shorter sides of a right-angled triangle are 24 cm and 18 cm. How long is the longest side (in cm)?
  16. 16.An exterior angle of a triangle is 79°. One of its two interior opposite angles is 22°. What is the other one (in degrees)?
  17. 17.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  18. 18.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)?
  19. 19.Can a triangle have sides of 12 cm, 10 cm and 8 cm? (a) Yes (b) No
  20. 20.The two shorter sides of a right-angled triangle are 12 cm and 16 cm. How long is the longest side (in cm)?
  21. 21.In triangle ABC, angle A = 86° and angle B = 29°. What is angle C (in degrees)?
  22. 22.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  23. 23.An exterior angle of a triangle is 90°. One of its two interior opposite angles is 63°. What is the other one (in degrees)?
  24. 24.In a right-angled triangle, one of the other two angles is 75°. What is the third angle (in degrees)?
  25. 25.Can a triangle have sides of 6 cm, 21 cm and 10 cm? (a) No (b) Yes
  26. 26.The longest side of a right-angled triangle is 26 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  27. 27.In a right-angled triangle, one of the other two angles is 42°. What is the third angle (in degrees)?
  28. 28.In an isosceles triangle, the two equal angles are 77° each. What is the third angle (in degrees)?
  29. 29.In an isosceles triangle, the two equal angles are 46° each. What is the third angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 41°. What is the third angle (in degrees)?
  31. 31.In an isosceles triangle, the two equal angles are 61° each. What is the third angle (in degrees)?
  32. 32.In triangle ABC, angle A = 89° and angle B = 26°. What is angle C (in degrees)?
  33. 33.Can a triangle have sides of 9 cm, 10 cm and 5 cm? (a) No (b) Yes
  34. 34.In triangle ABC, angle A = 37° and angle B = 88°. What is angle C (in degrees)?
  35. 35.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  36. 36.Can a triangle have sides of 7 cm, 12 cm and 21 cm? (a) No (b) Yes
  37. 37.In a right-angled triangle, one of the other two angles is 54°. What is the third angle (in degrees)?
  38. 38.Can a triangle have sides of 9 cm, 2 cm and 5 cm? (a) No (b) Yes
  39. 39.In a right-angled triangle, one of the other two angles is 58°. What is the third angle (in degrees)?
  40. 40.An exterior angle of a triangle is 103°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?

Answer key

  1. 12
  2. 17
  3. 65
  4. 29
  5. 20
  6. 63
  7. 72
  8. 72
  9. 63
  10. 67
  11. 23
  12. 22
  13. 33
  14. 62
  15. 30
  16. 57
  17. 120
  18. 7
  19. Yes
  20. 20
  21. 65
  22. 20
  23. 27
  24. 15
  25. No
  26. 10
  27. 48
  28. 26
  29. 88
  30. 49
  31. 58
  32. 65
  33. Yes
  34. 55
  35. 75
  36. No
  37. 36
  38. No
  39. 32
  40. 77

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