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Find the measure of angle A. 56° 3x + 13 1+ 7x O 150° O 70° O 46° O 78°

Find the measure of angle A. 56° 3x + 13 1+ 7x O 150° O 70° O 46° O 78°

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 the Measure of Angle A** In this problem, you are tasked with finding the measure of angle A in a triangle. The image presents a triangle with the following information: - One angle measures \(56^\circ\). - The second angle is expressed as \(3x + 13\). - Angle A is expressed as \(1 + 7x\). ### Answer Choices: - \(150^\circ\) - \(70^\circ\) - \(46^\circ\) - \(78^\circ\) ### Explanation: The sum of the angles in any triangle is \(180^\circ\). To find angle A, follow these steps: 1. Write the equation for the sum of the triangle's angles: \[ 56 + (3x + 13) + (1 + 7x) = 180 \] 2. Simplify and solve the equation to find \(x\). 3. Substitute \(x\) back into the expression for angle A \(1 + 7x\) to determine its measure. 4. Select the correct answer from the given choices.
Transcribed Image Text:**Find the Measure of Angle A** In this problem, you are tasked with finding the measure of angle A in a triangle. The image presents a triangle with the following information: - One angle measures \(56^\circ\). - The second angle is expressed as \(3x + 13\). - Angle A is expressed as \(1 + 7x\). ### Answer Choices: - \(150^\circ\) - \(70^\circ\) - \(46^\circ\) - \(78^\circ\) ### Explanation: The sum of the angles in any triangle is \(180^\circ\). To find angle A, follow these steps: 1. Write the equation for the sum of the triangle's angles: \[ 56 + (3x + 13) + (1 + 7x) = 180 \] 2. Simplify and solve the equation to find \(x\). 3. Substitute \(x\) back into the expression for angle A \(1 + 7x\) to determine its measure. 4. Select the correct answer from the given choices.
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