In a cyclic quadrilateral one set of opposite angles are in the ratio of 2 : 3, then the angles are
In a cyclic quadrilateral one set of opposite angles are in the ratio of 2 : 3, then the angles are
A) 40° 60°
B) 60°, 90°
C) 90°, 135°
D) 72° , 108°
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Correct option is (D) 72°, 108°
Let angles are 2x and 3x.
Then 2x+3x = \(108^\circ\) \((\because\) Sum of opposite angles in a cyclic quadrilateral is \(180^\circ)\)
\(\Rightarrow\) 5x = \(108^\circ\)
\(\Rightarrow\) x = \(\frac{180^\circ}5=36^\circ\)
\(\therefore\) \(2x=72^\circ\;and\;3x=108^\circ\)
Hence, required angles are \(72^\circ\;and\;108^\circ.\)
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