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O (x+3) (x-1)⁰ (x+1) •

O (x+3) (x-1)⁰ (x+1) •

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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**Title: Solving Angles in a Geometric Diagram** **Instructions:** Solve for \( x \) and then list the three angle measures. **Diagram Explanation:** The image contains a geometric diagram with three angles originating from a common point, resembling a triangle. These angles are denoted as: - \( (x+3)^\circ \) - \( (x-1)^\circ \) - \( (x+1)^\circ \) The sum of the angles in such a construction totals 90 degrees as they seem to form a right angle with the horizontal baseline. **Objective:** To find the value of \( x \) by solving the equation based on the angle sum and then calculate the measure of each angle. **Equation:** \[ (x+3) + (x-1) + (x+1) = 90 \] **Steps to Solve:** 1. Combine like terms in the equation: \[ 3x + 3 = 90 \] 2. Subtract 3 from both sides: \[ 3x = 87 \] 3. Divide by 3: \[ x = 29 \] **Angle Measures:** 1. \( (x+3)^\circ = (29+3)^\circ = 32^\circ \) 2. \( (x-1)^\circ = (29-1)^\circ = 28^\circ \) 3. \( (x+1)^\circ = (29+1)^\circ = 30^\circ \) These calculations verify the angle measures as parts of a right angle configuration.
Transcribed Image Text:**Title: Solving Angles in a Geometric Diagram** **Instructions:** Solve for \( x \) and then list the three angle measures. **Diagram Explanation:** The image contains a geometric diagram with three angles originating from a common point, resembling a triangle. These angles are denoted as: - \( (x+3)^\circ \) - \( (x-1)^\circ \) - \( (x+1)^\circ \) The sum of the angles in such a construction totals 90 degrees as they seem to form a right angle with the horizontal baseline. **Objective:** To find the value of \( x \) by solving the equation based on the angle sum and then calculate the measure of each angle. **Equation:** \[ (x+3) + (x-1) + (x+1) = 90 \] **Steps to Solve:** 1. Combine like terms in the equation: \[ 3x + 3 = 90 \] 2. Subtract 3 from both sides: \[ 3x = 87 \] 3. Divide by 3: \[ x = 29 \] **Angle Measures:** 1. \( (x+3)^\circ = (29+3)^\circ = 32^\circ \) 2. \( (x-1)^\circ = (29-1)^\circ = 28^\circ \) 3. \( (x+1)^\circ = (29+1)^\circ = 30^\circ \) These calculations verify the angle measures as parts of a right angle configuration.
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