Question

How to solve this question?

Answer 1

Given,

AB and CD are two equal chords

Therefore,

OP = OQ

Hence, angle OPQ = angle OQP ( angles opposite to equal sides of a triangle are equal)

Now,

angle POQ + angle OPQ + angle OQP = 180° (angle sum property of a triangle)

Putting the values,

150° + 2angle OPQ = 180°

2angle OPQ = 180° - 150°

2angle OPQ = 30°

angle OPQ = 30°/2

angle OPQ = 15°

Now,

angle OPA = 90° (given)

As we know,

angle OPQ + angle APQ = 90° (angle sum)

Putting the values,

15° + angle APQ = 90°

angle APQ = 90° - 15°

angle APQ = 75°

Therefore, the correct answer is option (b) 75°