Homework Help is Here – Start Your Trial Now!
Math
Geometry
What is the value of x? H - F x+18 I

What is the value of x? H - F x+18 I

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
See similar textbooks
icon
Related questions
Question
100%
### Understanding Angle Measures in a Cyclic Quadrilateral #### Problem Statement: **What is the value of \( x \)?** #### Diagram Description: The diagram shows a cyclic quadrilateral inscribed in a circle. The vertices of the quadrilateral are labeled \( G, F, H, \) and \( I \), with the points arranged consecutively along the circle. The specific angle measures provided in the diagram are: - \( \angle GHF = 2x \) - \( \angle FGI = x+18 \) #### Explanation: To find the value of \( x \), we should recall the properties of a cyclic quadrilateral: 1. **Opposite Angles of Cyclic Quadrilateral**: The opposite angles of a cyclic quadrilateral sum up to \( 180^\circ \). Using this property: Given the opposite angles \( \angle GHF \) and \( \angle FGI \): \[ 2x + (x + 18) = 180^\circ \] 2. **Solving for \( x \)**: Combine the terms and solve for \( x \): \[ 3x + 18 = 180^\circ \] \[ 3x = 162^\circ \] \[ x = \frac{162^\circ}{3} \] \[ x = 54^\circ \] Thus, the value of \( x \) is: \[ x = 54^\circ \] This problem demonstrates the use of properties of cyclic quadrilaterals to solve for unknown angle measures, emphasizing the importance of understanding these geometric principles.
Transcribed Image Text:### Understanding Angle Measures in a Cyclic Quadrilateral #### Problem Statement: **What is the value of \( x \)?** #### Diagram Description: The diagram shows a cyclic quadrilateral inscribed in a circle. The vertices of the quadrilateral are labeled \( G, F, H, \) and \( I \), with the points arranged consecutively along the circle. The specific angle measures provided in the diagram are: - \( \angle GHF = 2x \) - \( \angle FGI = x+18 \) #### Explanation: To find the value of \( x \), we should recall the properties of a cyclic quadrilateral: 1. **Opposite Angles of Cyclic Quadrilateral**: The opposite angles of a cyclic quadrilateral sum up to \( 180^\circ \). Using this property: Given the opposite angles \( \angle GHF \) and \( \angle FGI \): \[ 2x + (x + 18) = 180^\circ \] 2. **Solving for \( x \)**: Combine the terms and solve for \( x \): \[ 3x + 18 = 180^\circ \] \[ 3x = 162^\circ \] \[ x = \frac{162^\circ}{3} \] \[ x = 54^\circ \] Thus, the value of \( x \) is: \[ x = 54^\circ \] This problem demonstrates the use of properties of cyclic quadrilaterals to solve for unknown angle measures, emphasizing the importance of understanding these geometric principles.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer