Question
If arc mFG=60 degrees, then what is the measure of ∠FDG?(1 point) degrees
Answers
GPT-4o mini
To find the measure of angle \(\angle FDG\), we need to understand the relationship between the arc \(mFG\) and the angle formed by points \(F\), \(D\), and \(G\).
Given that the measure of arc \(mFG\) is \(60^\circ\), we can use the relationship between the arc and the inscribed angle. The inscribed angle theorem states that an inscribed angle is half the measure of the intercepted arc.
Thus, if arc \(mFG\) measures \(60^\circ\), the inscribed angle \(\angle FDG\) that intercepts arc \(FG\) would be:
\[
\angle FDG = \frac{1}{2} \times mFG = \frac{1}{2} \times 60^\circ = 30^\circ
\]
Therefore, \(\angle FDG\) measures \(30^\circ\).
So, the answer is **30 degrees**.
Given that the measure of arc \(mFG\) is \(60^\circ\), we can use the relationship between the arc and the inscribed angle. The inscribed angle theorem states that an inscribed angle is half the measure of the intercepted arc.
Thus, if arc \(mFG\) measures \(60^\circ\), the inscribed angle \(\angle FDG\) that intercepts arc \(FG\) would be:
\[
\angle FDG = \frac{1}{2} \times mFG = \frac{1}{2} \times 60^\circ = 30^\circ
\]
Therefore, \(\angle FDG\) measures \(30^\circ\).
So, the answer is **30 degrees**.