PAQ is a tangent to a circle with centre O, at a point A on it. AB is a chord such that ∠BAQ = xº (x < 90). C is a point on the major arc AB such that ∠ACB = yº. If ∠ABO = 32º , then the value of x + y is:
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Correct answer: D
Explanation
The correct answer is Option 4 i.e 116
We know that, in △ABO,
∠ABO = ∠OAB = 32º
So,
∠AOB = 180º - (32º + 32º) = 116º
Now,
∠ACB = y = 116/2 = 58º (Angle subtended by a chord at the centre is twice the angle subtended by it anywhere else)
So,
xº + yº = (90º - 32º) + 58º = 116º