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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 971 · 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 66°. What is the third angle (in degrees)?
  2. 2.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  3. 3.An exterior angle of a triangle is 113°. One of its two interior opposite angles is 64°. What is the other one (in degrees)?
  4. 4.Can a triangle have sides of 6 cm, 5 cm and 2 cm? (a) No (b) Yes
  5. 5.Can a triangle have sides of 13 cm, 6 cm and 2 cm? (a) No (b) Yes
  6. 6.In triangle ABC, angle A = 59° and angle B = 92°. What is angle C (in degrees)?
  7. 7.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  8. 8.In an isosceles triangle, the two equal angles are 29° each. What is the third angle (in degrees)?
  9. 9.In an isosceles triangle, the two equal angles are 26° each. What is the third angle (in degrees)?
  10. 10.The longest side of a right-angled triangle is 5 cm and one of the other sides is 3 cm. How long is the third side (in cm)?
  11. 11.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  12. 12.In an isosceles triangle, the angle between the two equal sides is 96°. What is each of the other two angles (in degrees)?
  13. 13.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  14. 14.The two interior opposite angles of a triangle are 59° and 55°. What is the exterior angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  16. 16.The two interior opposite angles of a triangle are 61° and 65°. What is the exterior angle (in degrees)?
  17. 17.In an isosceles triangle, the two equal angles are 30° each. What is the third angle (in degrees)?
  18. 18.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)?
  19. 19.An exterior angle of a triangle is 115°. One of its two interior opposite angles is 47°. What is the other one (in degrees)?
  20. 20.In an isosceles triangle, the two equal angles are 63° each. What is the third angle (in degrees)?
  21. 21.An exterior angle of a triangle is 138°. One of its two interior opposite angles is 74°. What is the other one (in degrees)?
  22. 22.In triangle ABC, angle A = 97° and angle B = 34°. What is angle C (in degrees)?
  23. 23.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)?
  24. 24.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  25. 25.In triangle ABC, angle A = 63° and angle B = 23°. What is angle C (in degrees)?
  26. 26.An exterior angle of a triangle is 124°. One of its two interior opposite angles is 51°. What is the other one (in degrees)?
  27. 27.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)?
  28. 28.In an isosceles triangle, the two equal angles are 28° each. What is the third angle (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  30. 30.In triangle ABC, angle A = 63° and angle B = 40°. What is angle C (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 79°. What is the third angle (in degrees)?
  32. 32.An exterior angle of a triangle is 91°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  34. 34.An exterior angle of a triangle is 101°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  35. 35.In triangle ABC, angle A = 42° and angle B = 59°. What is angle C (in degrees)?
  36. 36.In an isosceles triangle, the angle between the two equal sides is 52°. What is each of the other two angles (in degrees)?
  37. 37.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  38. 38.The two interior opposite angles of a triangle are 30° and 20°. What is the exterior angle (in degrees)?
  39. 39.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  40. 40.In triangle ABC, angle A = 72° and angle B = 67°. What is angle C (in degrees)?

Answer key

  1. 24
  2. 40
  3. 49
  4. Yes
  5. No
  6. 29
  7. 45
  8. 122
  9. 128
  10. 4
  11. 90
  12. 42
  13. 25
  14. 114
  15. 62
  16. 126
  17. 120
  18. 15
  19. 68
  20. 54
  21. 64
  22. 49
  23. 10
  24. 100
  25. 94
  26. 73
  27. 12
  28. 124
  29. 25
  30. 77
  31. 11
  32. 36
  33. 21
  34. 51
  35. 79
  36. 64
  37. 84
  38. 50
  39. 54
  40. 41

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