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x does not equal degrees; don't' forget to add degrees in with your ang 10. P x= R X= m/P m/PQR 61 58° m/P = 61° = m/PQR= 61° (2x) Q X X S X

x does not equal degrees; don't' forget to add degrees in with your ang 10. P x= R X= m/P m/PQR 61 58° m/P = 61° = m/PQR= 61° (2x) Q X X S X

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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**Problem 10:** Consider the triangle \( \triangle PQR \) with the following angle measures: - \( \angle RPQ = x^\circ \) - \( \angle PRQ = 58^\circ \) - \( \angle PQR = (2x)^\circ \) Find the following: - \( x = \_\_\_ \) - \( m\angle P = \_\_\_ \) - \( m\angle PQR = \_\_\_ \) *Solution provided:* 1. \( x = 61 \) ❌ 2. \( m\angle P = 61^\circ \) ❌ 3. \( m\angle PQR = 61^\circ \) ❌ **Explanation of the Diagram:** The diagram shows a triangle \( \triangle PQR \) with vertex \( P \) at the top. The triangle has two given angles: \( \angle PRQ = 58^\circ \) located at vertex \( R \), and \( \angle PQR = (2x)^\circ \) located at vertex \( Q \). The angle \( \angle RPQ = x^\circ \) is at vertex \( P \). The goal is to solve for \( x \) and determine the measures of the specified angles using the information provided. Given that the sum of angles in any triangle is \( 180^\circ \), calculations should utilize this property to find the unknown values accurately. The marked solutions are demonstrated to be incorrect, as the cross "❌" indicates errors in the provided answers.
Transcribed Image Text:**Problem 10:** Consider the triangle \( \triangle PQR \) with the following angle measures: - \( \angle RPQ = x^\circ \) - \( \angle PRQ = 58^\circ \) - \( \angle PQR = (2x)^\circ \) Find the following: - \( x = \_\_\_ \) - \( m\angle P = \_\_\_ \) - \( m\angle PQR = \_\_\_ \) *Solution provided:* 1. \( x = 61 \) ❌ 2. \( m\angle P = 61^\circ \) ❌ 3. \( m\angle PQR = 61^\circ \) ❌ **Explanation of the Diagram:** The diagram shows a triangle \( \triangle PQR \) with vertex \( P \) at the top. The triangle has two given angles: \( \angle PRQ = 58^\circ \) located at vertex \( R \), and \( \angle PQR = (2x)^\circ \) located at vertex \( Q \). The angle \( \angle RPQ = x^\circ \) is at vertex \( P \). The goal is to solve for \( x \) and determine the measures of the specified angles using the information provided. Given that the sum of angles in any triangle is \( 180^\circ \), calculations should utilize this property to find the unknown values accurately. The marked solutions are demonstrated to be incorrect, as the cross "❌" indicates errors in the provided answers.
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