Question

a circle is centered on point b. points a, c and d lie on its circumference.
if \\( \angle abc \\) measures \\( 122^\circ \\), what does \\( \angle adc \\) measure?
\\( \square ^\circ \\)

Explanation:

Step1: Recall the central angle theorem

The central angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc. Here, \(\angle ABC\) is a central angle subtending arc \(AC\), and \(\angle ADC\) is an inscribed angle subtending the same arc \(AC\).

Step2: Calculate the measure of \(\angle ADC\)

Given that \(\angle ABC = 122^\circ\), we use the relationship from the central angle theorem. The measure of the inscribed angle \(\angle ADC\) is half of the central angle \(\angle ABC\). So we calculate:
\[
\angle ADC=\frac{1}{2}\times\angle ABC
\]
Substitute \(\angle ABC = 122^\circ\) into the formula:
\[
\angle ADC=\frac{1}{2}\times122^\circ = 61^\circ
\]

Answer:

\(61\)