To understand this, first, let us understand what is a segment and what are types of segments. Any chord drawn in a circle divides the circle into two segments. A major segment and a minor segment. The major segment is so called because it covers a major portion of the circle and its arc length is higher than the other. Conversely, a minor segment is so called because its arc length is smaller and covers a smaller portion of the circle (Note: if chord happens to be a diameter, then both these segments are same and are called semicircular segments)
A circle segment is a slice made by a chord of a circle, Basically, a segment is a region that lies between a chord a circle and its associated arc. Thus, when a single chord is drawn in a circle is divided into two segments. The smaller segment is known as the minor segment while the larger one is known as the major segment.
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Each segment is called alternate segment of the other.
So if you have an angle in a Minor segment, the angle in the alternate segment will lie in Major segment and vice versa.