in the adjoining figure, ABCD is a cyclic quadrilateral. Find a the value of x.
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We know, in a cyclic quadrilateral, the sum of opposite angles are supplementary, i.e. 180
o
.
Here, ABCD is a cyclic quadrilateral.
Then,
∠A+∠C=180
∘
⟹ 2x+14
o
+4x+4
o
=180
∘
⟹ 6x+18
o
=180
∘
⟹ 6x=180
∘
−18
o
⟹ 6x=162
o
⟹ x=27
o
.
Also,
∠B+∠D=180
∘
(Sum of opposite angles of cyclic quadrilateral =180
∘
)
⟹ 5y+5
o
+50
o
=180
o
⟹ 5y=180
o
−55
o
⟹ 5y=125
o
⟹ y=25
o
.
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