We want to know the measure of the angle ADB on the circle D.
For doing so, we remember that:
• The measure of an inscribed angle is ,half ,of the measure of the arcs it intercepts.
,
• The measure of an arc is ,equal ,to the measure of the central angle it generates (whose vertex is the center of the circle).
In the graph, we see that the angle ACB is inscribed, and thus, the measure of the arc AB is given by:
[tex]\hat{AB}=2m\angle ACB=2\cdot(57^{\circ})=114^{\circ}[/tex]
But, the arc AB is equal to the central angle it generates, this is:
[tex]\hat{AB}=m\angle ADB=114^{\circ}[/tex]
This means that the measure of ∠ADB is 114°.
