Mathematics
In the given figure, ABCD is a cyclic quadrilateral. The measure of its greatest angle is :
135°
140°
150°
160°
Circles
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Answer
The sum of the opposite angles of a cyclic quadrilateral is 180°.
∠A + ∠C = 180°
y + 5y = 180°
6y = 180°
y = 30°
∠B + ∠D = 180°
3x + x = 180°
4x = 180°
x = 45°
∠A = y = 30°
∠C = 5y = 150°
∠D = x = 45°
∠B = 3x = 135°
Hence, option 3 is the correct option.
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