B. Y A C Note: Figure is not drawn to scale In the triangle above, the measure of ZA is 40°, and the measure of ZB is 83°. What is the measure of ZC? 49°
B. Y A C Note: Figure is not drawn to scale In the triangle above, the measure of ZA is 40°, and the measure of ZB is 83°. What is the measure of ZC? 49°
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Geometry Problem: Finding the Measure of an Angle in a Triangle
#### Problem Statement
In the triangle above, the measure of ∠A is 40°, and the measure of ∠B is 83°.
**Question**: What is the measure of ∠C?
#### Answer Choices
- **A**. 49°
- **B**. 53°
- **C**. 57°
- **D**. 61°
#### Explanation
In the given triangle, the vertices are labeled as A, B, and C with sides labeled X, Y, and Z. The measures of angles A and B are given as 40° and 83° respectively.
Since the sum of the interior angles of a triangle is always 180°, we can find the measure of ∠C using the formula:
\[ \text{Sum of angles} = ∠A + ∠B + ∠C = 180° \]
Plugging in the given values:
\[ 40° + 83° + ∠C = 180° \]
Solving for ∠C:
\[ ∠C = 180° - (40° + 83°) \]
\[ ∠C = 180° - 123° \]
\[ ∠C = 57° \]
Therefore, the measure of ∠C is **57°**.
So, the correct answer is:
- **C. 57°**
### Diagram Description
The diagram shows a triangle with vertices marked as A, B, and C. Side X is opposite vertex C, side Y is opposite vertex A, and side Z is opposite vertex B. The triangle is not drawn to scale, which is indicated in the note below the figure.
This exercise tests the understanding of the properties of a triangle, specifically the sum of its interior angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b4ac02d-8fa9-4cd1-ad8a-49ffeef4197d%2F4f6891cd-ea00-4905-acf6-95ad3691920f%2Fa3jjrws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding the Measure of an Angle in a Triangle
#### Problem Statement
In the triangle above, the measure of ∠A is 40°, and the measure of ∠B is 83°.
**Question**: What is the measure of ∠C?
#### Answer Choices
- **A**. 49°
- **B**. 53°
- **C**. 57°
- **D**. 61°
#### Explanation
In the given triangle, the vertices are labeled as A, B, and C with sides labeled X, Y, and Z. The measures of angles A and B are given as 40° and 83° respectively.
Since the sum of the interior angles of a triangle is always 180°, we can find the measure of ∠C using the formula:
\[ \text{Sum of angles} = ∠A + ∠B + ∠C = 180° \]
Plugging in the given values:
\[ 40° + 83° + ∠C = 180° \]
Solving for ∠C:
\[ ∠C = 180° - (40° + 83°) \]
\[ ∠C = 180° - 123° \]
\[ ∠C = 57° \]
Therefore, the measure of ∠C is **57°**.
So, the correct answer is:
- **C. 57°**
### Diagram Description
The diagram shows a triangle with vertices marked as A, B, and C. Side X is opposite vertex C, side Y is opposite vertex A, and side Z is opposite vertex B. The triangle is not drawn to scale, which is indicated in the note below the figure.
This exercise tests the understanding of the properties of a triangle, specifically the sum of its interior angles.
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