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In quadrilateral ABCD, if ∠A = 60 and ∠B : ∠C : ∠D = 2:3:7, then ∠D is :
  • a)
    25
  • b)
    175
  • c)
    180
  • d)
    50
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In quadrilateral ABCD, if∠A =60 and∠B :∠C :∠D = 2:3:7,...
Given in quadrilateral ABCD:
  • ∠A = 60°
  • Ratio ∠B : ∠C : ∠D = 2:3:7
We let:
  • ∠B = 2x
  • ∠C = 3x
  • ∠D = 7x
Since the sum of the angles in a quadrilateral is 360°, we have:
∠A + ∠B + ∠C + ∠D = 360° 60° + 2x + 3x + 7x = 360° 12x + 60° = 360° 12x = 300° x = 25°
Substituting back to find ∠D:
∠D = 7x = 7 × 25° = 175°
Thus, ∠D is 175°.
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In quadrilateral ABCD, if∠A =60 and∠B :∠C :∠D = 2:3:7,...
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In quadrilateral ABCD, if∠A =60 and∠B :∠C :∠D = 2:3:7,...
In quadrilateral ABCD, if AB = CD and AD = BC, then we can conclude that the quadrilateral is a parallelogram.
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