Question

if $\angle adc$ measures $62^\circ$, what does $\angle abc$ measure? \boxed{} $^\circ$

Explanation:

Step1: Apply the inscribed - angle theorem

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

Step2: Calculate \(\angle ABC\)

We know that if \(\theta_{inscribed}\) is the measure of an inscribed angle and \(\theta_{central}\) is the measure of the central angle subtending the same arc, then \(\theta_{central}=2\theta_{inscribed}\). Given \(\theta_{inscribed}=\angle ADC = 62^{\circ}\), so \(\angle ABC=2\times62^{\circ}\)

Answer:

\(124\)