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### Measuring and Constructing Angles #### Problem 9 Given that ∠EFG is a right angle, find \( m∠EFH \) and \( m∠HFG \). #### Diagram Explanation The diagram shows a right angle ∠EFG. - **Point E** is located on the left vertical arm of the angle, extending upwards. - **Point F** is at the vertex of the right angle. - The segment FG is horizontal, extending to the right. - **Point H** is on the ray FH, forming two angles with the initial right angle: ∠EFH and ∠HFG. **Angle Measurements:** - ∠EFH is labeled as \((2x + 2)^\circ\). - ∠HFG is labeled as \((x + 1)^\circ\). ### Task Use the information given and the properties of right angles to find the measures of \( m∠EFH \) and \( m∠HFG \). Note that the sum of these angles must equal 90°, as ∠EFG is a right angle.

### Measuring and Constructing Angles #### Problem 9 Given that ∠EFG is a right angle, find \( m∠EFH \) and \( m∠HFG \). #### Diagram Explanation The diagram shows a right angle ∠EFG. - **Point E** is located on the left vertical arm of the angle, extending upwards. - **Point F** is at the vertex of the right angle. - The segment FG is horizontal, extending to the right. - **Point H** is on the ray FH, forming two angles with the initial right angle: ∠EFH and ∠HFG. **Angle Measurements:** - ∠EFH is labeled as \((2x + 2)^\circ\). - ∠HFG is labeled as \((x + 1)^\circ\). ### Task Use the information given and the properties of right angles to find the measures of \( m∠EFH \) and \( m∠HFG \). Note that the sum of these angles must equal 90°, as ∠EFG is a right angle.

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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### Measuring and Constructing Angles #### Problem 9 Given that ∠EFG is a right angle, find \( m∠EFH \) and \( m∠HFG \). #### Diagram Explanation The diagram shows a right angle ∠EFG. - **Point E** is located on the left vertical arm of the angle, extending upwards. - **Point F** is at the vertex of the right angle. - The segment FG is horizontal, extending to the right. - **Point H** is on the ray FH, forming two angles with the initial right angle: ∠EFH and ∠HFG. **Angle Measurements:** - ∠EFH is labeled as \((2x + 2)^\circ\). - ∠HFG is labeled as \((x + 1)^\circ\). ### Task Use the information given and the properties of right angles to find the measures of \( m∠EFH \) and \( m∠HFG \). Note that the sum of these angles must equal 90°, as ∠EFG is a right angle.
Transcribed Image Text:### Measuring and Constructing Angles #### Problem 9 Given that ∠EFG is a right angle, find \( m∠EFH \) and \( m∠HFG \). #### Diagram Explanation The diagram shows a right angle ∠EFG. - **Point E** is located on the left vertical arm of the angle, extending upwards. - **Point F** is at the vertex of the right angle. - The segment FG is horizontal, extending to the right. - **Point H** is on the ray FH, forming two angles with the initial right angle: ∠EFH and ∠HFG. **Angle Measurements:** - ∠EFH is labeled as \((2x + 2)^\circ\). - ∠HFG is labeled as \((x + 1)^\circ\). ### Task Use the information given and the properties of right angles to find the measures of \( m∠EFH \) and \( m∠HFG \). Note that the sum of these angles must equal 90°, as ∠EFG is a right angle.
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