Angles in the same segment - Higher
The angles at the Circumference is the name of the perimeter of a complete circle, that is, the distance all around it. An angle created by an object at a given point. by the same arc are equal.
Put more simply, angles in the same segment are equal.
Angles \(a = a\)
Example
Calculate the angles \(p\) and \(q\).
Angles in the same segment are equal.
\(p = 52^\circ\)
\(q = 40^\circ\)
Proof
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.