Question

question 20 (5 points)
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in the above figure, \\( \angle aob = 80 ^ { \circ } \\). what does \\( \angle acb \\) equal?

Explanation:

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

The measure of an inscribed angle (\(\angle ACB\)) subtended by an arc is half the measure of the central angle (\(\angle AOB\)) subtended by the same arc.
The formula is \(\angle ACB=\frac{1}{2}\angle AOB\).

Step2: Substitute the given value of \(\angle AOB\)

Given \(\angle AOB = 80^{\circ}\).
Substitute into the formula: \(\angle ACB=\frac{1}{2}\times80^{\circ}\).

Answer:

\(40^{\circ}\)