Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Certainly! Below is the transcription of the text and the detailed explanation of the diagram. --- ### 4. Solve for \( x \). #### Diagram Explanation: The diagram depicts a circle with center \( I \) and points \( E, F, G, H \) positioned on the circumference. - **Angle \(\angle EIF = 68^\circ\)** - **Angle \(\angle EGH = (9x - 5)^\circ\)** The objective is to solve for \( x \). **Details of the Diagram:** - Point \( E \) and point \( F \) are endpoints of a chord within the circle. - Point \( G \) is situated on the circumference, and \( \angle EGH \) involves points \( E \), \( G \), and \( H \). - The circle is intersected in such a way that creates the two given angles. ### Problem-Solving Steps: 1. Given that \( \angle EIF = 68^\circ \) is an inscribed angle. 2. Because \( \angle EGH \) subtends the same arc \( \overarc{EH} \) as \( \angle EIF \), the angles have a relationship due to the inscribed angle theorem. The inscribed angle theorem states that if two inscribed angles of a circle intercept the same arc, then the angles are equal. Thus, \[ \angle EGH = \angle EIF \] Substituting the values, \[ (9x - 5)^\circ = 68^\circ \] Solving for \( x \): \[ 9x - 5 = 68 \] \[ 9x = 68 + 5 \] \[ 9x = 73 \] \[ x = \frac{73}{9} \] \[ x = \frac{73}{9} = 8.11 \text{ (approx)} \] ### Conclusion: The value of \( x \) is approximately \( 8.11 \). --- This text and diagram explanation can help students understand how to solve for \( x \) in the given geometric context.
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Transcribed Image Text:Certainly! Below is the transcription of the text and the detailed explanation of the diagram. --- ### 4. Solve for \( x \). #### Diagram Explanation: The diagram depicts a circle with center \( I \) and points \( E, F, G, H \) positioned on the circumference. - **Angle \(\angle EIF = 68^\circ\)** - **Angle \(\angle EGH = (9x - 5)^\circ\)** The objective is to solve for \( x \). **Details of the Diagram:** - Point \( E \) and point \( F \) are endpoints of a chord within the circle. - Point \( G \) is situated on the circumference, and \( \angle EGH \) involves points \( E \), \( G \), and \( H \). - The circle is intersected in such a way that creates the two given angles. ### Problem-Solving Steps: 1. Given that \( \angle EIF = 68^\circ \) is an inscribed angle. 2. Because \( \angle EGH \) subtends the same arc \( \overarc{EH} \) as \( \angle EIF \), the angles have a relationship due to the inscribed angle theorem. The inscribed angle theorem states that if two inscribed angles of a circle intercept the same arc, then the angles are equal. Thus, \[ \angle EGH = \angle EIF \] Substituting the values, \[ (9x - 5)^\circ = 68^\circ \] Solving for \( x \): \[ 9x - 5 = 68 \] \[ 9x = 68 + 5 \] \[ 9x = 73 \] \[ x = \frac{73}{9} \] \[ x = \frac{73}{9} = 8.11 \text{ (approx)} \] ### Conclusion: The value of \( x \) is approximately \( 8.11 \). --- This text and diagram explanation can help students understand how to solve for \( x \) in the given geometric context.
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