Angles in the same segment

Angles standing on the same arc from the circumference are equal.

Key formulas

If ∠ACB and ∠ADB both stand on arc AB, they are equal.

One inscribed angle is 47°. Another on the same arc is also 47°, even if the chords look different.

Angles in the opposite segment are not equal to these; they stand on the other arc.

Problem. ∠ACB and ∠ADB stand on the same arc AB. If ∠ACB = 47°, find ∠ADB.

Solution. Angles in the same segment are equal, so ∠ADB = 47°.

Each equals half the angle at the centre on the same arc.

One angle in a segment is 61°. Another on the same arc is:

Yes — the arms go to the endpoints of the arc.