Question

a circle is centered on point b. points a, c and d lie on its circumference. if ∠abc measures 46°, what does ∠adc measure? °

Explanation:

Step1: Recall the central - inscribed angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Identify the central and inscribed angles

Here, \(\angle ABC\) is a central angle and \(\angle ADC\) is an inscribed angle subtending the same arc \(AC\).

Step3: Calculate the measure of \(\angle ADC\)

Since the measure of an inscribed angle \(=\frac{1}{2}\times\) measure of the central angle, and \(\angle ABC = 46^{\circ}\), then \(\angle ADC=\frac{1}{2}\times\angle ABC\).
\(\angle ADC=\frac{1}{2}\times46^{\circ}\)

Answer:

\(23\)