Question

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

Explanation:

Step1: Recall arc - angle relationship

The measure of an arc is equal to the measure of the central angle that subtends it. The measure of the entire circle is 360°.

Step2: Find the measure of arc $DGF$

The central angle $\angle DEF = 70^{\circ}$, and the arc $DF$ has a measure of 70°. The arc $DGF$ is the major arc. The measure of arc $DGF=360^{\circ}-\text{measure of arc }DF$.
So, $\text{measure of arc }DGF = 360 - 70=290^{\circ}$.

Answer:

D. 290°