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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Transcribed Image Text:### Problem 34: Quadrilateral Angle Measurement
**Objective:**
Find the measure of angle \( \angle G \).
**Question:**
Find \( m\angle G \).
**Diagram:**
A quadrilateral \( EFGH \) is shown with the following details:
- Angle \( E \) (denoted as \( \angle E \)) measures 60 degrees.
- Angle \( H \) (denoted as \( \angle H \)) measures 110 degrees.
- Each side of the quadrilateral is marked with small ticks, indicating that all sides are of equal length.
**Choices:**
- 60 degrees
- 80 degrees
- 110 degrees
- 360 degrees
To answer the question, use the properties of the quadrilateral and the provided angle measures.
**Explanation Diagram:**
The provided diagram shows a rhombus \( EFGH \). In a rhombus, opposite angles are equal, and adjacent angles are supplementary.
Given the angle measures:
- \( \angle E = 60^\circ \)
- \( \angle H = 110^\circ \)
Since \( EFGH \) is a rhombus, the opposite angles must be equal:
- \( \angle G = \angle E = 60^\circ \)
- Following the properties of the rhombus, \( \angle F \) would be supplementary to \( \angle E \) and \( \angle H \), which implies \( \angle F = 180^\circ - 60^\circ = 120^\circ \).
**Conclusion:**
The measure of \( \angle G \) is 60 degrees.
**Correct Answer:**
- 60 degrees
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