Question

in circle b with ( mangle adc = 21^{circ} ), find the measure of minor arc ( overarc{ac} ).

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. That is, if \(\angle ADC\) is an inscribed angle and \(\overset{\frown}{AC}\) is the intercepted arc, then \(m\angle ADC=\frac{1}{2}m\overset{\frown}{AC}\).

Step2: Solve for \(m\overset{\frown}{AC}\)

Given \(m\angle ADC = 21^{\circ}\), from the formula \(m\overset{\frown}{AC}=2\times m\angle ADC\).
Substitute \(m\angle ADC = 21^{\circ}\) into the formula: \(m\overset{\frown}{AC}=2\times21^{\circ}\).

Answer:

\(42^{\circ}\)