what is m∠g? write your answer as an integer or decimal. m∠g = °
what is m∠g? write your answer as an integer or decimal. m∠g = °
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, the inscribed angle $\angle DFE = 34^{\circ}$, and the central angle $\angle DGE$ subtends the same arc $\overset{\frown}{DE}$.
Step2: Calculate the measure of $\angle DGE$
By the inscribed - angle theorem, if the measure of the inscribed angle $\theta_{i}$ and the central angle $\theta_{c}$ subtend the same arc, then $\theta_{c}=2\theta_{i}$. So, $m\angle G = 2\times m\angle DFE$. Since $m\angle DFE = 34^{\circ}$, then $m\angle G=2\times34^{\circ}=68^{\circ}$.
Answer:
$68$