Question
If arc mFG=60 degrees, then what is the measure of ∠FDG ? (1 point)
Answers
GPT-4o mini
To find the measure of angle ∠FDG given that arc \( mFG = 60^\circ \), we can use the relationship between the measure of an arc and the angle it subtends at the center of the circle.
1. The angle subtended by an arc at the center of the circle is equal to the measure of the arc. Therefore, if \( mFG = 60^\circ \), then the angle \( ∠FOG \) (where O is the center of the circle) is also \( 60^\circ \).
2. If we consider point D to be any point on the circle, ∠FDG is an inscribed angle that subtends the same arc FG.
3. The measure of an inscribed angle is half the measure of the arc it subtends. Hence:
\[
∠FDG = \frac{1}{2} mFG = \frac{1}{2} \times 60^\circ = 30^\circ
\]
So, the measure of ∠FDG is \( 30^\circ \).
1. The angle subtended by an arc at the center of the circle is equal to the measure of the arc. Therefore, if \( mFG = 60^\circ \), then the angle \( ∠FOG \) (where O is the center of the circle) is also \( 60^\circ \).
2. If we consider point D to be any point on the circle, ∠FDG is an inscribed angle that subtends the same arc FG.
3. The measure of an inscribed angle is half the measure of the arc it subtends. Hence:
\[
∠FDG = \frac{1}{2} mFG = \frac{1}{2} \times 60^\circ = 30^\circ
\]
So, the measure of ∠FDG is \( 30^\circ \).