Question

in circle b with ( mangle abc = 48^{circ} ), find the ( mangle adc ).

Explanation:

Step1: Recall the central - angle and inscribed - angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. In circle \(B\), \(\angle ABC\) is a central angle and \(\angle ADC\) is an inscribed angle. Both angles subtend arc \(AC\).

Step2: Apply the formula

We know that \(m\angle ADC=\frac{1}{2}m\angle ABC\). Given \(m\angle ABC = 48^{\circ}\).
Substitute the value of \(m\angle ABC\) into the formula: \(m\angle ADC=\frac{1}{2}\times48^{\circ}\).

Answer:

\(24^{\circ}\)