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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 25 · 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 interior opposite angles of a triangle are 30° and 24°. What is the exterior angle (in degrees)?
  2. 2.In an isosceles triangle, the angle between the two equal sides is 74°. What is each of the other two angles (in degrees)?
  3. 3.The longest side of a right-angled triangle is 15 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  4. 4.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  6. 6.Can a triangle have sides of 8 cm, 7 cm and 20 cm? (a) Yes (b) No
  7. 7.In an isosceles triangle, the two equal angles are 59° each. What is the third angle (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  9. 9.The two interior opposite angles of a triangle are 73° and 52°. What is the exterior angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 68°. What is the third angle (in degrees)?
  11. 11.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  12. 12.In triangle ABC, angle A = 83° and angle B = 51°. What is angle C (in degrees)?
  13. 13.The two interior opposite angles of a triangle are 51° and 24°. What is the exterior angle (in degrees)?
  14. 14.In triangle ABC, angle A = 92° and angle B = 62°. What is angle C (in degrees)?
  15. 15.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  16. 16.In triangle ABC, angle A = 84° and angle B = 30°. What is angle C (in degrees)?
  17. 17.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles (in degrees)?
  19. 19.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)?
  20. 20.In triangle ABC, angle A = 83° and angle B = 32°. What is angle C (in degrees)?
  21. 21.In triangle ABC, angle A = 89° and angle B = 58°. What is angle C (in degrees)?
  22. 22.In triangle ABC, angle A = 29° and angle B = 109°. What is angle C (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 37°. What is the third angle (in degrees)?
  24. 24.Can a triangle have sides of 3 cm, 18 cm and 10 cm? (a) No (b) Yes
  25. 25.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  26. 26.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)?
  27. 27.In triangle ABC, angle A = 51° and angle B = 20°. What is angle C (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 48°. What is each of the other two angles (in degrees)?
  29. 29.The two interior opposite angles of a triangle are 54° and 72°. What is the exterior angle (in degrees)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 126°. What is each of the other two angles (in degrees)?
  31. 31.An exterior angle of a triangle is 123°. One of its two interior opposite angles is 67°. What is the other one (in degrees)?
  32. 32.Can a triangle have sides of 22 cm, 8 cm and 9 cm? (a) Yes (b) No
  33. 33.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  34. 34.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  35. 35.An exterior angle of a triangle is 140°. One of its two interior opposite angles is 79°. What is the other one (in degrees)?
  36. 36.An exterior angle of a triangle is 64°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  37. 37.The longest side of a right-angled triangle is 5 cm and one of the other sides is 4 cm. How long is the third side (in cm)?
  38. 38.An exterior angle of a triangle is 105°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  39. 39.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles (in degrees)?
  40. 40.In triangle ABC, angle A = 63° and angle B = 23°. What is angle C (in degrees)?

Answer key

  1. 54
  2. 53
  3. 9
  4. 40
  5. 80
  6. No
  7. 62
  8. 67
  9. 125
  10. 22
  11. 72
  12. 46
  13. 75
  14. 26
  15. 50
  16. 66
  17. 90
  18. 65
  19. 15
  20. 65
  21. 33
  22. 42
  23. 53
  24. No
  25. 20
  26. 24
  27. 109
  28. 66
  29. 126
  30. 27
  31. 56
  32. No
  33. 10
  34. 45
  35. 61
  36. 40
  37. 3
  38. 47
  39. 35
  40. 94

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