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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**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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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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