2) Angles in the same segment
The angles at the circumference subtended by the same arc are equal. Put more simply, angles in the same segment are equal.
Angle α = α.
Calculate the angles p and q.
Angles in the same segment are equal. So p = 52° and q = 40°
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.