the angles of a quadrilateral are2x,2x+15,4x-12 and 3x-0.5.Find the value of x and all the angles of the quadrilateral.
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The angles of a quadrilateral are 2x,2x+15,4x−12 and 3x+5. Find the value of x and all angles of the quadrilateral.
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Given angles of a quadrilateral are 2x,2x+15,4x−12,3x+5
As we know that, sum of all interior angles in a quadrilateral is equal to 360
∘
.
2x+2x+15+4x−12+3x+5=360
⇒11x+8=360
⇒11x=360−8
⇒11x=352
⇒x=32
(i) 2x=2(32)
=64
(ii) 2x+15=64+15
=79
(iii) 4x−12=4(32)−12
=128−12
=116
(iv) 3x−0.5=3(32)+5
=101
So, the angles of the quadrilateral are 65
∘
,80
∘
,118
∘
,97
∘
.
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