Question
UV
is tangent to ⨀T. What is m∠V?
T
U
V
69°
m∠V=
°
is tangent to ⨀T. What is m∠V?
T
U
V
69°
m∠V=
°
Answers
GPT-4o mini
To find the measure of angle \( m\angle V \), we need to use properties of tangents to circles.
If \( UV \) is tangent to circle \( T \) at point \( V \), the angle formed between the tangent line \( UV \) and the radius \( TV \) is \( 90^\circ \). If we are given that \( m\angle UVT = 69^\circ \), we can find \( m\angle V \).
Since:
\[
m\angle UVT + m\angle V = 90^\circ
\]
We can substitute in what we know:
\[
69^\circ + m\angle V = 90^\circ
\]
Now we can solve for \( m\angle V \):
\[
m\angle V = 90^\circ - 69^\circ = 21^\circ
\]
So, the measure of angle \( V \) is:
\[
m\angle V = 21^\circ
\]
If \( UV \) is tangent to circle \( T \) at point \( V \), the angle formed between the tangent line \( UV \) and the radius \( TV \) is \( 90^\circ \). If we are given that \( m\angle UVT = 69^\circ \), we can find \( m\angle V \).
Since:
\[
m\angle UVT + m\angle V = 90^\circ
\]
We can substitute in what we know:
\[
69^\circ + m\angle V = 90^\circ
\]
Now we can solve for \( m\angle V \):
\[
m\angle V = 90^\circ - 69^\circ = 21^\circ
\]
So, the measure of angle \( V \) is:
\[
m\angle V = 21^\circ
\]