Question

how does the measure of angle cad compare to the measure of angle dbc?
none of these.
the measure of angle cad is equal to the measure of angle dbc.
the measure of angle cad is half as big as the measure of angle dbc.
the measure of angle cad is twice as big as the measure of angle dbc.

Explanation:

Step1: Recall the inscribed - angle theorem

In a circle, inscribed angles that subtend the same arc are equal.

Step2: Identify the arcs subtended by the angles

Angle \(CAD\) and angle \(DBC\) subtend the same arc \(CD\).
By the inscribed - angle theorem, \(\angle CAD=\angle DBC\) since they are inscribed angles subtending the same arc \(CD\) in the given circle.

Answer:

The measure of angle CAD is equal to the measure of angle DBC.