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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 346 · 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 28°. What is the third angle (in degrees)?
  2. 2.The two interior opposite angles of a triangle are 66° and 69°. What is the exterior angle (in degrees)?
  3. 3.An exterior angle of a triangle is 103°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  4. 4.In triangle ABC, angle A = 76° and angle B = 30°. What is angle C (in degrees)?
  5. 5.The two interior opposite angles of a triangle are 54° and 68°. What is the exterior angle (in degrees)?
  6. 6.Can a triangle have sides of 5 cm, 3 cm and 3 cm? (a) Yes (b) No
  7. 7.In triangle ABC, angle A = 67° and angle B = 23°. What is angle C (in degrees)?
  8. 8.The two interior opposite angles of a triangle are 46° and 20°. What is the exterior angle (in degrees)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 34°. What is each of the other two angles (in degrees)?
  10. 10.The two interior opposite angles of a triangle are 38° and 23°. What is the exterior angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  12. 12.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  13. 13.In an isosceles triangle, the angle between the two equal sides is 64°. What is each of the other two angles (in degrees)?
  14. 14.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)?
  15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle (in degrees)?
  16. 16.The two interior opposite angles of a triangle are 23° and 27°. What is the exterior angle (in degrees)?
  17. 17.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 114°. What is each of the other two angles (in degrees)?
  19. 19.In an isosceles triangle, the two equal angles are 36° each. What is the third angle (in degrees)?
  20. 20.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  21. 21.In a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  22. 22.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  23. 23.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  24. 24.In triangle ABC, angle A = 91° and angle B = 31°. What is angle C (in degrees)?
  25. 25.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  26. 26.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  27. 27.In a right-angled triangle, one of the other two angles is 75°. What is the third angle (in degrees)?
  28. 28.In triangle ABC, angle A = 76° and angle B = 36°. What is angle C (in degrees)?
  29. 29.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 42°. What is the third angle (in degrees)?
  31. 31.In triangle ABC, angle A = 43° and angle B = 24°. What is angle C (in degrees)?
  32. 32.An exterior angle of a triangle is 144°. One of its two interior opposite angles is 71°. What is the other one (in degrees)?
  33. 33.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)?
  34. 34.An exterior angle of a triangle is 108°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  35. 35.An exterior angle of a triangle is 88°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  36. 36.In triangle ABC, angle A = 42° and angle B = 29°. What is angle C (in degrees)?
  37. 37.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)?
  38. 38.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  39. 39.The two interior opposite angles of a triangle are 76° and 77°. What is the exterior angle (in degrees)?
  40. 40.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?

Answer key

  1. 62
  2. 135
  3. 31
  4. 74
  5. 122
  6. Yes
  7. 90
  8. 66
  9. 73
  10. 61
  11. 31
  12. 30
  13. 58
  14. 15
  15. 100
  16. 50
  17. 48
  18. 33
  19. 108
  20. 13
  21. 21
  22. 90
  23. 45
  24. 58
  25. 66
  26. 25
  27. 15
  28. 68
  29. 35
  30. 48
  31. 113
  32. 73
  33. 24
  34. 75
  35. 55
  36. 109
  37. 10
  38. 54
  39. 153
  40. 90

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