Question

if ∠def measures 70°, what is the measure of 𝐷𝐺𝐹? a. 290° b. 140° c. 220° d. 70°

Explanation:

Step1: Recall arc - central angle relationship

The measure of an arc is equal to the measure of its central angle. The sum of the measures of the arcs of a circle is 360°.

Step2: Identify given central angle

The central angle ∠DEF = 70°, and the arc associated with it is $\overset{\frown}{DF}$.

Step3: Calculate the measure of $\overset{\frown}{DGF}$

The measure of $\overset{\frown}{DGF}=360^{\circ}-\text{measure of }\overset{\frown}{DF}$. Since the measure of $\overset{\frown}{DF}$ is equal to the measure of ∠DEF (70°), then the measure of $\overset{\frown}{DGF}=360 - 70=290^{\circ}$.

Answer:

A. 290°