Question
Points and lines are marked on a circle with a center point labeled upper W.
The mYZ=93°
. Find m∠ZXY
.
The mYZ=93°
. Find m∠ZXY
.
Answers
GPT-4o mini
To find \( m\angle ZXY \), we need to understand how the angles relate to one another on the circle.
Given that \( m\angle YZW = 93^\circ \) is the angle at point \( Z \) formed by lines extending to points \( Y \) and \( W \) (the center of the circle), we can use one of the properties of inscribed angles to find \( m\angle ZXY \).
1. **Identify the type of angle**: Since \( W \) is the center of the circle, \( YW \) and \( ZW \) are radii of the circle.
2. **Understand the relationship**: The angle \( ZXY \) is an inscribed angle that subtends the same arc as the central angle \( YZW \). The inscribed angle is half the measure of the central angle subtending the same arc.
3. **Calculate**: Since \( m\angle YZW = 93^\circ \), the inscribed angle \( m\angle ZXY \) will be:
\[
m\angle ZXY = \frac{1}{2} m\angle YZW = \frac{1}{2} \times 93^\circ = 46.5^\circ.
\]
So, \( m\angle ZXY = 46.5^\circ \).
Given that \( m\angle YZW = 93^\circ \) is the angle at point \( Z \) formed by lines extending to points \( Y \) and \( W \) (the center of the circle), we can use one of the properties of inscribed angles to find \( m\angle ZXY \).
1. **Identify the type of angle**: Since \( W \) is the center of the circle, \( YW \) and \( ZW \) are radii of the circle.
2. **Understand the relationship**: The angle \( ZXY \) is an inscribed angle that subtends the same arc as the central angle \( YZW \). The inscribed angle is half the measure of the central angle subtending the same arc.
3. **Calculate**: Since \( m\angle YZW = 93^\circ \), the inscribed angle \( m\angle ZXY \) will be:
\[
m\angle ZXY = \frac{1}{2} m\angle YZW = \frac{1}{2} \times 93^\circ = 46.5^\circ.
\]
So, \( m\angle ZXY = 46.5^\circ \).