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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