In the given figure, PQ is the tangent to the circle XYZ at X. if XYZ = 220°, how much is m<PXY ?

We are given that \( PQ \) is the tangent to the circle XYZ at point \( X \), and the measure of the arc \( XYZ \) is \( 220^\circ \).

To find \( m\angle PXY \), we can use the following concept:

1. **Angle Between Tangent and Chord**: The measure of the angle formed between a tangent and a chord at the point of contact is equal to half the measure of the intercepted arc. 

In this case, \( \angle PXY \) is the angle between the tangent \( PQ \) and the chord \( XY \), and the intercepted arc is \( XYZ \).

The intercepted arc \( XYZ \) is given as \( 220^\circ \).

Thus, the measure of \( m\angle PXY \) is:
\[
m\angle PXY = \frac{1}{2} \times m(\text{arc } XYZ)
\]
\[
m\angle PXY = \frac{1}{2} \times 220^\circ = 110^\circ
\]

Therefore, the measure of \( m\angle PXY \) is \( 110^\circ \).

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Would you like a detailed explanation of how tangent and chord properties work? 

Here are 5 related questions to expand on this topic:

1. What is the relationship between a tangent and a radius at the point of contact?
2. How do you calculate angles in a cyclic quadrilateral?
3. What is the measure of an angle formed by two intersecting chords inside a circle?
4. How is the central angle related to the intercepted arc of a circle?
5. What is the difference between a secant and a tangent in circle geometry?

**Tip**: In any circle, the angle formed by a tangent and a chord through the point of contact is always half the measure of the intercepted arc.

In the given figure, PQ is the tangent to the circle XYZ at X. if XYZ = 220°, how much is m<PXY?

Learn how to calculate the angle PXY between a tangent and a chord in a circle where the arc XYZ is 220°. This problem demonstrates the Angle Between Tangent and Chord Theorem and provides a clear step-by-step solution. Suitable for students in Grades 9-10.

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