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In quadrilateral ABCD, ∠B=90, ∠C−∠D = 60 and ∠A−∠C−∠D = 10. Find ∠A, ∠C and ∠D.
  • a)
    140, 95, 35
  • b)
    145, 55, 20
  • c)
    150, 60, 80
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In quadrilateral ABCD,∠B=90,∠C−∠D = 60 and∠A&min...
∠B = 90°
∠C - ∠D = 60°
∠A - ∠C - ∠D = 10°.......(1)
∠A + ∠C + ∠D = 360° - 90° = 270° (from Angle sum property of quadrilateral)
On adding,
∠A + ∠C + ∠D = 270°
∠A - ∠C - ∠D = 10°
2∠A = 280°
∠A = 140°
=> from (1)
∠A = 140°, ∠A - (∠C + ∠D) = 10°
140° - (∠C + ∠D) = 10°
∠C + ∠D = 130° ...........(2)
If ∠C - ∠D = 60° & ∠C + ∠D = 130°
2∠C = 190°, ∠C = 95°
∠D = 130° - 95° - from (2)
∠D = 35°
So, the correct answer is option (a).
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Most Upvoted Answer
In quadrilateral ABCD,∠B=90,∠C−∠D = 60 and∠A&min...
There are four sides and four angles. The sum of the angles in a quadrilateral is 360 degrees.
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Community Answer
In quadrilateral ABCD,∠B=90,∠C−∠D = 60 and∠A&min...
Because the angle triangle is scale triangle
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