Question

In the given circle with centre O, what is the measure of $\angle ONP$ ?

Statement I: $\angle OMN = 31^\circ$ Statement II: $\angle NMP = 98^\circ$

Choose: (a) if the question can be answered by one statement alone, but cannot be answered by using the other statement alone. (b) if the question can be answered by using either statement alone. (c) if the question can be answered by using both the statements together but cannot be answered by using either statement alone. (d) if the question cannot be answered even by using both the statements together.

Accepted Answer

C. To find $\angle ONP$ in triangle $	riangle ONP$ or $	riangle MNP$ inscribed in the circle, both angle relations $\angle OMN$ and $\angle NMP$ are required to determine the angles subtended at the center/circumference. Together they allow solving for $\angle ONP$.

Data Sufficiency - Angle in a Circle

Explanation

Practise this under exam conditions