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Find x. (4x + 10) 40°

Find x. (4x + 10) 40°

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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**Find x.** The image shows an isosceles triangle with one of the base angles labeled as \(40^\circ\). The apex angle, indicated with an expression, is \( (4x + 10)^\circ \). ### Explanation: In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal. Given: - The base angles of the triangle are equal. Since one base angle is \(40^\circ\), the other base angle is also \(40^\circ\). - The sum of the angles in any triangle is \(180^\circ\). Thus, we can write the equation: \[ 40 + 40 + (4x + 10) = 180 \] Simplify and solve for \(x\): 1. Combine the known angles: \[ 80 + (4x + 10) = 180 \] 2. Combine like terms: \[ 4x + 90 = 180 \] 3. Subtract 90 from both sides: \[ 4x = 90 \] 4. Divide both sides by 4: \[ x = 22.5 \] **Answer: \(x = 22.5\)**
Transcribed Image Text:**Find x.** The image shows an isosceles triangle with one of the base angles labeled as \(40^\circ\). The apex angle, indicated with an expression, is \( (4x + 10)^\circ \). ### Explanation: In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal. Given: - The base angles of the triangle are equal. Since one base angle is \(40^\circ\), the other base angle is also \(40^\circ\). - The sum of the angles in any triangle is \(180^\circ\). Thus, we can write the equation: \[ 40 + 40 + (4x + 10) = 180 \] Simplify and solve for \(x\): 1. Combine the known angles: \[ 80 + (4x + 10) = 180 \] 2. Combine like terms: \[ 4x + 90 = 180 \] 3. Subtract 90 from both sides: \[ 4x = 90 \] 4. Divide both sides by 4: \[ x = 22.5 \] **Answer: \(x = 22.5\)**
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