It is important to know the theorems well and to learn to identify them in the diagrams. The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply ...

Let the obtuse angle MOQ = \(2x\). Using the circle theorem, the angle at the centre is twice the angle at the circumference. Angle MNQ = \(x\) and angle MPQ = \(x\). Therefore angle MNQ = angle MPQ.