What will be the value of the angle (in degrees) subtended by the chord in the minor segment of the circle, if the length of a chord is equal to the radius of the circle?

Let the radius of the circle be r. The length of the chord AB is also given as r.
In △OAB (where O is the center of the circle):

OA=OB=AB=r
Therefore, △OAB is an equilateral triangle.
The angle subtended by the chord at the center is ∠AOB=60
∘
.

The angle subtended by the chord in the major segment (∠ACB, where C lies on the major arc) is half of the angle subtended at the center:

∠ACB=
2
60
∘

​
=30
∘

Let D be a point on the minor arc. Then ADBC forms a cyclic quadrilateral.
In a cyclic quadrilateral, the sum of opposite angles is 180
∘
:

∠ADB+∠ACB=180
∘

∠ADB+30
∘
=180
∘

∠ADB=180
∘
−30
∘
=150
∘

Thus, the angle subtended by the chord in the minor segment is 150
∘
.