When calculating angles using a circle theorem, always state which theorem ... which meet at the same point are the same length. Angles in a triangle add up to 180°.

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.