Question

circle d is shown in the diagram below. ∠abc is an inscribed angle, and ( moverarc{ac} ) is ( 98^circ ). what is ( mangle abc )?

Explanation:

Step1: Recall the inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So, if \( m\widehat{AC} = 98^\circ \), then the inscribed angle \( \angle ABC \) that intercepts arc \( AC \) will have a measure equal to half of \( 98^\circ \).

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

Using the formula from the inscribed angle theorem, \( m\angle ABC=\frac{1}{2}m\widehat{AC} \). Substituting \( m\widehat{AC} = 98^\circ \) into the formula, we get \( m\angle ABC=\frac{1}{2}\times98^\circ \).
Calculating \( \frac{98}{2} = 49 \), so \( m\angle ABC = 49^\circ \).

Answer:

\( 49 \)