34. Find the indicated measure. * Find m/G. %23 E 60 110 H. O 60 degrees 80 degrees O 110 degrees 360 degrees

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
icon
Related questions
Topic Video
Question
please help
### 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
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning