Question 68
ABCD is cyclic quadrilateral in which $$\angle$$A = x$$^\circ$$, $$\angle$$B = 5y$$^\circ$$, $$\angle$$C = 2x$$^\circ$$ and $$\angle$$D = y$$^\circ$$. What is the value of (3x - y)?
Solution
ABCD is cyclic quadrilateral.
Opposite angles in a cyclic quadrilateral are supplementary.
$$\angle$$A + $$\angle$$C = 180$$^\circ$$
x + 2x = 180$$^\circ$$
3x = 180$$^\circ$$
x = 60$$^\circ$$
$$\angle$$B + $$\angle$$D = 180$$^\circ$$
5y + y = 180$$^\circ$$
6y = 180$$^\circ$$
y = 30$$^\circ$$
3x - y = 3(60) - 30 = 150
Hence, the correct answer is Option C
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