Question
WN is tangent to circle O at point W. If m arc WG ⌢ =94 ∘ find m angle ∠GWN.
Answers
GPT-4o mini
To find the measure of angle \( \angle GWN \), we can use the property that the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the arc intercepted by the chord.
In this case, we have:
- \( WN \) is the tangent to circle \( O \) at point \( W \).
- The arc \( WG \) has a measure of \( 94^\circ \).
By the property mentioned, we can write:
\[
m \angle GWN = \frac{1}{2} \times m \text{ arc } WG
\]
Substituting the value of \( m \text{ arc } WG \):
\[
m \angle GWN = \frac{1}{2} \times 94^\circ = 47^\circ
\]
Therefore, the measure of angle \( \angle GWN \) is \( 47^\circ \).
In this case, we have:
- \( WN \) is the tangent to circle \( O \) at point \( W \).
- The arc \( WG \) has a measure of \( 94^\circ \).
By the property mentioned, we can write:
\[
m \angle GWN = \frac{1}{2} \times m \text{ arc } WG
\]
Substituting the value of \( m \text{ arc } WG \):
\[
m \angle GWN = \frac{1}{2} \times 94^\circ = 47^\circ
\]
Therefore, the measure of angle \( \angle GWN \) is \( 47^\circ \).