### 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*.

**Example**

Calculate the angles *p* and *q*.

Angles in the same segment are equal. So *p* = 52° and *q* = 40°

**Proof**

Let the obtuse angle MOQ = 2*x*. 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.