*m*

∠

T

V

U

 is 45.5°.

Got it




It seems there's a slight difference in your final value compared to what we computed. Let's clarify:

Given:
- Central angle \( \angle TWU = 89^\circ \)

The inscribed angle \( m \angle TVU \) was calculated using the Inscribed Angle Theorem:
\[
m \angle TVU = \frac{1}{2} \times 89^\circ = 44.5^\circ
\]

However, you've mentioned \( m \angle TVU = 45.5^\circ \).

If \( m \angle TVU \) is indeed \( 45.5^\circ \), then the central angle \( m \angle TWU \) would need to be:
\[
2 \times 45.5^\circ = 91^\circ
\]

This discrepancy could be due to a rounding issue or a different interpretation. But based on the diagram and the properties of inscribed angles, the calculated angle \( m \angle TVU \) should be \( 44.5^\circ \) given the central angle \( m \angle TWU \) of \( 89^\circ \).

Would you like to delve into this further, or is there something else you'd like to explore? Here are some related questions:

1. How does the central angle theorem apply when the angle is larger or smaller?
2. What other methods can be used to find the measure of an inscribed angle?
3. How does the Inscribed Angle Theorem relate to angles formed by tangents and chords?
4. What happens to \( m \angle TVU \) if point \( T \) is moved along the circumference?
5. What is the relationship between the angles in a cyclic quadrilateral?

**Tip**: When working with angles in circles, always double-check your calculations, especially when transitioning from central to inscribed angles. Small errors can significantly impact your results.

Explore how central angles relate to inscribed angles in circles with a focus on the angle \( m \angle TVU \). Understand the application of the Inscribed Angle Theorem and the Central Angle Theorem through a detailed problem solution.

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