A chord of a circle is equal to its radius. The angle subtended by this chord at a point in the major segment is:

We know that the angle subtended by a chord at the centre of a circle is double of that at the circumference.

Let PQ is the chord of a circle with centre O.

∴ PQ = OP = OQ 

Therefore, △POQ is an equilateral triangle.

So, ∠POQ = 60^o 

We know that the angle subtended by a chord at the centre is twice the same at the circumference.

∴ ∠PRQ = $\frac{1}{2}$∠POQ = $\frac{1}{2}\times {60}^o={30}^o$ 

 Hence, the angle subtended by the chord at a point in the major segment is 30^o.