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Drag the correct symbols into each box to create an expression for the measure, in degrees, of ZXY Z. 1 2 3

Drag the correct symbols into each box to create an expression for the measure, in degrees, of ZXY Z. 1 2 3

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Drag the correct symbols into each box to create an expression for the measure, in degrees, of <XYZ,

### Angle Measurement in a Circle In the given diagram, we see a circle with center \( O \) and an angle \( \angle XYZ \) inscribed in the circle. The circle also includes points \( X \), \( Y \), and \( Z \). The task is to determine the measure, in degrees, of \( \angle XYZ \) by creating an expression using the provided symbols. #### Step-by-Step Explanation: 1. **Understanding the Diagram**: - **Diagram Description**: - Point \( O \) is the center of the circle. - \( XYZ \) is an inscribed angle in the circle. - \( k^\circ \) represents the angle at point \( X \) from the center \( O \) to point \( Z \). 2. **Objective**: - To find the measure of \( \angle XYZ \), an expression needs to be constructed using the choices provided. 3. **Given Choices**: - **Symbols provided** for creating the expression are: - Numbers: \( 90 \), \( 180 \) - Operations: \( + \), \( - \) - Variables: \( \frac{1}{2}k \), \( k \), \( 2k \) 4. **Drag and Drop Boxes**: - There are three boxes labeled \( 1 \), \( 2 \), and \( 3 \) where the correct symbols need to be placed to form the correct expression. #### Construction of the Expression: To construct the expression, follow these steps: - \( \angle XYZ \) is an inscribed angle, and inscribed angles subtended by the same arc are half the measure of the central angle subtending the same arc. - Given \( k^\circ \) is the central angle at \( O \), the inscribed angle \( \angle XYZ \) is half of \( k \). Thus, the correct expression for \( \angle XYZ \) is: 1. Box 1: \( \frac{1}{2} k \) 2. Box 2: (Empty, since only one element is needed) 3. Box 3: (Empty, since only one element is needed) Hence, filling in just the first box with \( \frac{1}{2} k \) would provide the appropriate measure for \( \angle XYZ \). By understanding the relationship between central angles and inscribed angles
Transcribed Image Text:### Angle Measurement in a Circle In the given diagram, we see a circle with center \( O \) and an angle \( \angle XYZ \) inscribed in the circle. The circle also includes points \( X \), \( Y \), and \( Z \). The task is to determine the measure, in degrees, of \( \angle XYZ \) by creating an expression using the provided symbols. #### Step-by-Step Explanation: 1. **Understanding the Diagram**: - **Diagram Description**: - Point \( O \) is the center of the circle. - \( XYZ \) is an inscribed angle in the circle. - \( k^\circ \) represents the angle at point \( X \) from the center \( O \) to point \( Z \). 2. **Objective**: - To find the measure of \( \angle XYZ \), an expression needs to be constructed using the choices provided. 3. **Given Choices**: - **Symbols provided** for creating the expression are: - Numbers: \( 90 \), \( 180 \) - Operations: \( + \), \( - \) - Variables: \( \frac{1}{2}k \), \( k \), \( 2k \) 4. **Drag and Drop Boxes**: - There are three boxes labeled \( 1 \), \( 2 \), and \( 3 \) where the correct symbols need to be placed to form the correct expression. #### Construction of the Expression: To construct the expression, follow these steps: - \( \angle XYZ \) is an inscribed angle, and inscribed angles subtended by the same arc are half the measure of the central angle subtending the same arc. - Given \( k^\circ \) is the central angle at \( O \), the inscribed angle \( \angle XYZ \) is half of \( k \). Thus, the correct expression for \( \angle XYZ \) is: 1. Box 1: \( \frac{1}{2} k \) 2. Box 2: (Empty, since only one element is needed) 3. Box 3: (Empty, since only one element is needed) Hence, filling in just the first box with \( \frac{1}{2} k \) would provide the appropriate measure for \( \angle XYZ \). By understanding the relationship between central angles and inscribed angles
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