Question

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

Explanation:

Step1: Recall the property of central and inscribed angles

In a circle, the central angle (angle \(ABC\) with vertex at the center \(B\)) and the inscribed angle (angle \(BAD\) with vertex on the circumference) subtended by the same arc \(CD\).

Step2: Apply the central - inscribed angle relationship

The measure of an inscribed angle is half of the measure of the central angle subtended by the same arc. Let the measure of arc \(CD\) be \(x\). The measure of the central angle \(\angle ABC\) is equal to the measure of arc \(CD\) (by the definition of central angle). The measure of the inscribed angle \(\angle BAD=\frac{1}{2}\) measure of arc \(CD\). So \(\angle ABC = 2\angle BAD\).

Answer:

The measure of angle ABC is twice as big as the measure of angle BAD.