In the diagram below, AD || EH, m/I = 50° and mZFBC = 47°. Find MZIGF. Step Angle Reason mZI 50° Given 2 MZFBC 47 Given try Select a Reason So G H. A B D

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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In the diagram below, \( \overline{AD} \parallel \overline{EH}, m\angle I = 50^\circ \) and \( m\angle FBC = 47^\circ \). Find \( m\angle IGF \).

**Step-by-step solution:**

| Step | Angle             | Reason |
|------|-------------------|--------|
| 1    | \( m\angle I = 50^\circ \) | Given  |
| 2    | \( m\angle FBC = 47^\circ \) | Given  |
| try  | \( m\angle IGF = \) | Select a Reason |

**Diagram Explanation:**

The diagram shows a geometric figure with the following details:
- \( \overline{AD} \) and \( \overline{EH} \) are parallel lines.
- Point \( I \) is above the line \( \overline{EF} \), with \( \angle I \) marked as \( 50^\circ \).
- Points B, C, D, and H are collinear along the line \( \overline{BCDEH} \).
- \( \angle FBC \) is marked as \( 47^\circ \).
- The task is to find \( m\angle IGF \).

The parallel lines and marked angles suggest the need to use the properties of parallel lines and transversals or potentially relationships between interior and exterior angles of triangles.
Transcribed Image Text:In the diagram below, \( \overline{AD} \parallel \overline{EH}, m\angle I = 50^\circ \) and \( m\angle FBC = 47^\circ \). Find \( m\angle IGF \). **Step-by-step solution:** | Step | Angle | Reason | |------|-------------------|--------| | 1 | \( m\angle I = 50^\circ \) | Given | | 2 | \( m\angle FBC = 47^\circ \) | Given | | try | \( m\angle IGF = \) | Select a Reason | **Diagram Explanation:** The diagram shows a geometric figure with the following details: - \( \overline{AD} \) and \( \overline{EH} \) are parallel lines. - Point \( I \) is above the line \( \overline{EF} \), with \( \angle I \) marked as \( 50^\circ \). - Points B, C, D, and H are collinear along the line \( \overline{BCDEH} \). - \( \angle FBC \) is marked as \( 47^\circ \). - The task is to find \( m\angle IGF \). The parallel lines and marked angles suggest the need to use the properties of parallel lines and transversals or potentially relationships between interior and exterior angles of triangles.
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