three angles of quadrilateral are in ratio 2 :3 :4 the sum of least and the greatest of these angles is equal to 180 degree find all the angles of this quadrilateral
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The sum of interior angles of a quadrilateral ABCD= 360°
Let the angles be: ∠A,∠B,∠Cand∠D.
∠A+∠B+∠C+∠D=360°
Let the common ratio bex, and then let ∠A:∠B:∠C=4x:5x:6x
Also, let ∠D=y
⇒∠A+∠B+∠C+∠D=4x+5x+6x+y=360°
⇒y=360°−15x.(1)
⇒4x+6x=160°.
⇒x=16
⇒∠A=4x=4∗16=64°
∠B=5x=5∗16=80°
∠C=6x=6∗16=96°
D=y=360°−15x=360 −15∗16=360−240°=120°
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