question about a circle property

a chord in a circle will always extend equal angles

but it will not extend equal angles if you exend into the other segment

(chord divides circle into a major and minor segment, all angles in minor segment are equal to each other but not equal to the chords in major segment)

am i correct so far?

now i want to know if there is a relation between the angle in the minor segment and the major segment. e.g. are they suplimentary angles?

thanks in advanced for any help!