An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended by the arc at a point on the circle?

Since the angle subtended by an arc at any point on the remaining part of the circle is half the angle subtended by the arc at the centre, the angle at the circumference is $\frac{70^{\circ}}{2} = 35^{\circ}$.

Concept Applied
The angle subtended by an arc at the centre is twice the angle it subtends at any point on the remaining part of the circle.