Question

a circle is centered on point b. points a, c and d lie on its circumference. if ∠adc measures 62°, what does ∠abc measure?

Explanation:

Step1: Recall the central - angle theorem

The central - angle theorem states that the measure of a central angle (\(\angle ABC\)) is twice the measure of an inscribed angle (\(\angle ADC\)) that subtends the same arc (\(\overset{\frown}{AC}\)).

Step2: Calculate \(\angle ABC\)

Given \(\angle ADC = 62^{\circ}\), using the formula \(\angle ABC=2\angle ADC\).
Substitute \(\angle ADC = 62^{\circ}\) into the formula: \(\angle ABC = 2\times62^{\circ}\).
\(\angle ABC=124^{\circ}\)

Answer:

\(124\)