Question

circle g is shown in the diagram below.
complete the paragraph.
in circle g, ∠dgf is ▲ and ∠def is ▲. the measure of ∠def is ▲ (the measure of ∠dgf.

Explanation:

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

The measure of an inscribed angle ($\angle DEF$) in a circle is half the measure of the central angle ($\angle DGF$) that subtends the same arc.

Step2: Assume the measure of $\angle DGF$

Let's assume the measure of $\angle DGF$ is $x$. Then the measure of $\angle DEF=\frac{1}{2}x$.

Answer:

In circle \( G\), \(\angle DGF\) is a central angle and \(\angle DEF\) is an inscribed angle. The measure of \(\angle DEF\) is half the measure of \(\angle DGF\).