Calculate the size of the angle marked m

The image shows a tangent to a circle and a chord originating from the point of tangency. The angle between the tangent and the chord is given, and we need to find an angle subtended by the chord in the alternate segment. This situation directly applies the Alternate Segment Theorem.

The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
In this diagram:

• The tangent is the line touching the circle at point A.
• The chord is AB.
• The angle between the tangent and the chord AB is given as $65^\circ$.
• The angle 'm' is the angle subtended by the chord AB at point C on the circumference, which is in the alternate segment.

Therefore, according to the theorem:
$m = 65^\circ$