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98 11. Kite WXYZ is inscribed in circle M. Vertices W and I are endpoints of a diameter of the circle and m/XWZ = 98⁰. Y Part A What is the measure of WZ in degrees? Part B What is the measure of WXY. in degrees?

98 11. Kite WXYZ is inscribed in circle M. Vertices W and I are endpoints of a diameter of the circle and m/XWZ = 98⁰. Y Part A What is the measure of WZ in degrees? Part B What is the measure of WXY. in degrees?

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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### Inscribed Kite and Angles **Problem Statement:** A kite \( WXYZ \) is inscribed in circle \( M \). Vertices \( W \) and \( Y \) are the endpoints of a diameter of the circle. Given that the measure of angle \( \angle XWZ \) is \( 98^\circ \), determine the following: #### Part A What is the measure of \( \angle WZ \) in degrees? #### Part B What is the measure of \( \angle WXY \) in degrees? **Diagram Explanation:** The provided diagram illustrates a circle with the kite \( WXYZ \) inscribed within it. The circle's diameter passes through points \( W \) and \( Y \). Points \( Z \) and \( X \) are located on the circumference of the circle. The angle at \( W \) (\( \angle XWZ \)) is denoted as \( 98^\circ \). Additional auxiliary lines from the center of the circle to points \( X \) and \( Z \) appear to be included to help with the depiction of the kite's symmetric properties. **Solution Steps:** 1. **Calculation for Part A:** - Since \( W \) and \( Y \) are endpoints of the diameter, triangle \( WZY \) is a right triangle (Inscribed Angle Theorem) and \( \angle WYZ \) is \( 90^\circ \). - Using the property of cyclic quadrilateral \( WXYZ \), the opposite angles \( \angle WZ \) and \( \angle WY \) sum up to \( 180^\circ \). 2. **Calculation for Part B:** - Using properties of circles and symmetry, calculate \( \angle WXY \) considering the cyclic nature of the quadrilateral and the other known angles. By exploring these relationships and properties, one can find the measured angles required for the specific parts of this problem. Construct your solution considering properties of inscribed angles, cyclic quadrilaterals, and basic geometric theorems. --- (*Insert mathematical properties, detailed steps, and solutions accordingly for educational purposes.*) ### Angle Calculation Guide Please note that detailed, step-by-step breakdowns are essential for demonstrating the reasoning and calculations to ensure a clear understanding of the geometric properties at play.
Transcribed Image Text:### Inscribed Kite and Angles **Problem Statement:** A kite \( WXYZ \) is inscribed in circle \( M \). Vertices \( W \) and \( Y \) are the endpoints of a diameter of the circle. Given that the measure of angle \( \angle XWZ \) is \( 98^\circ \), determine the following: #### Part A What is the measure of \( \angle WZ \) in degrees? #### Part B What is the measure of \( \angle WXY \) in degrees? **Diagram Explanation:** The provided diagram illustrates a circle with the kite \( WXYZ \) inscribed within it. The circle's diameter passes through points \( W \) and \( Y \). Points \( Z \) and \( X \) are located on the circumference of the circle. The angle at \( W \) (\( \angle XWZ \)) is denoted as \( 98^\circ \). Additional auxiliary lines from the center of the circle to points \( X \) and \( Z \) appear to be included to help with the depiction of the kite's symmetric properties. **Solution Steps:** 1. **Calculation for Part A:** - Since \( W \) and \( Y \) are endpoints of the diameter, triangle \( WZY \) is a right triangle (Inscribed Angle Theorem) and \( \angle WYZ \) is \( 90^\circ \). - Using the property of cyclic quadrilateral \( WXYZ \), the opposite angles \( \angle WZ \) and \( \angle WY \) sum up to \( 180^\circ \). 2. **Calculation for Part B:** - Using properties of circles and symmetry, calculate \( \angle WXY \) considering the cyclic nature of the quadrilateral and the other known angles. By exploring these relationships and properties, one can find the measured angles required for the specific parts of this problem. Construct your solution considering properties of inscribed angles, cyclic quadrilaterals, and basic geometric theorems. --- (*Insert mathematical properties, detailed steps, and solutions accordingly for educational purposes.*) ### Angle Calculation Guide Please note that detailed, step-by-step breakdowns are essential for demonstrating the reasoning and calculations to ensure a clear understanding of the geometric properties at play.
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