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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 854 · 40 sums
TalentJR

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 56°. What is the exterior angle (in degrees)?
  2. 2.The longest side of a right-angled triangle is 39 cm and one of the other sides is 36 cm. How long is the third side (in cm)?
  3. 3.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  4. 4.In triangle ABC, angle A = 84° and angle B = 69°. What is angle C (in degrees)?
  5. 5.Can a triangle have sides of 4 cm, 10 cm and 15 cm? (a) No (b) Yes
  6. 6.In triangle ABC, angle A = 61° and angle B = 30°. What is angle C (in degrees)?
  7. 7.In a right-angled triangle, one of the other two angles is 79°. What is the third angle (in degrees)?
  8. 8.In an isosceles triangle, the two equal angles are 57° each. What is the third angle (in degrees)?
  9. 9.In triangle ABC, angle A = 49° and angle B = 77°. What is angle C (in degrees)?
  10. 10.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  11. 11.In an isosceles triangle, the angle between the two equal sides is 108°. What is each of the other two angles (in degrees)?
  12. 12.The two interior opposite angles of a triangle are 55° and 44°. What is the exterior angle (in degrees)?
  13. 13.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  14. 14.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)?
  15. 15.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  16. 16.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  17. 17.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  18. 18.The two interior opposite angles of a triangle are 73° and 75°. What is the exterior angle (in degrees)?
  19. 19.Can a triangle have sides of 13 cm, 5 cm and 9 cm? (a) Yes (b) No
  20. 20.Can a triangle have sides of 8 cm, 10 cm and 19 cm? (a) Yes (b) No
  21. 21.The two shorter sides of a right-angled triangle are 18 cm and 24 cm. How long is the longest side (in cm)?
  22. 22.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  23. 23.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  24. 24.The longest side of a right-angled triangle is 30 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  25. 25.Can a triangle have sides of 7 cm, 2 cm and 6 cm? (a) No (b) Yes
  26. 26.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  27. 27.An exterior angle of a triangle is 104°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 64°. What is each of the other two angles (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 29°. What is the third angle (in degrees)?
  30. 30.Can a triangle have sides of 6 cm, 9 cm and 8 cm? (a) Yes (b) No
  31. 31.In an isosceles triangle, the two equal angles are 62° each. What is the third angle (in degrees)?
  32. 32.In triangle ABC, angle A = 36° and angle B = 72°. What is angle C (in degrees)?
  33. 33.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)?
  34. 34.Can a triangle have sides of 12 cm, 20 cm and 8 cm? (a) No (b) Yes
  35. 35.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  36. 36.An exterior angle of a triangle is 117°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  37. 37.Can a triangle have sides of 11 cm, 20 cm and 9 cm? (a) Yes (b) No
  38. 38.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 70°. What is the other one (in degrees)?
  39. 39.In an isosceles triangle, the angle between the two equal sides is 74°. What is each of the other two angles (in degrees)?
  40. 40.In triangle ABC, angle A = 36° and angle B = 85°. What is angle C (in degrees)?

Answer key

  1. 86
  2. 15
  3. 50
  4. 27
  5. No
  6. 89
  7. 11
  8. 66
  9. 54
  10. 17
  11. 36
  12. 99
  13. 36
  14. 7
  15. 100
  16. 18
  17. 57
  18. 148
  19. Yes
  20. No
  21. 30
  22. 17
  23. 72
  24. 18
  25. Yes
  26. 31
  27. 32
  28. 58
  29. 61
  30. Yes
  31. 56
  32. 72
  33. 15
  34. No
  35. 10
  36. 42
  37. No
  38. 25
  39. 53
  40. 59

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