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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Question
The figure shows a right triangle with one of its angles marked as \(x^\circ\) and the other non-right angle marked as \(150^\circ\) exterior to the triangle.
### Description of the Figure:
1. **Right Triangle**: The triangle is a right triangle, indicated by the right angle symbol at the base of the triangle.
2. **Exterior Angle**: The exterior angle adjacent to the base of the triangle is given as \(150^\circ\).
### Explanation of Angles in the Figure:
1. **Straight Line Property**: A straight line forms an angle of \(180^\circ\). The exterior angle of \(150^\circ\) and the interior angle adjacent to it (we'll call it \(y\)) form a straight line together.
Therefore, \(y = 180^\circ - 150^\circ = 30^\circ\).
2. **Sum of Angles in a Triangle**: The sum of the interior angles in a triangle is \(180^\circ\).
Given the right triangle:
- One angle is \(90^\circ\) (the right angle),
- Another angle is \(30^\circ\) (angle \(y\) calculated above),
- The third angle (our angle \(x\)) can be calculated as:
\[
x = 180^\circ - 90^\circ - 30^\circ = 60^\circ
\]
Hence, angle \(x\) measures \(60^\circ\).
### Conclusion:
By applying the properties of angles, we determined that the measure of angle \(x\) is \(60^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4895642d-adca-4243-b0c4-c741dfdd726d%2F0b8f7942-0830-4163-99ec-5cce83c28158%2Fi0f69oh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining the Measure of Angle x**
In the figure below, what is the measure of angle \(x^\circ\)?
The figure shows a right triangle with one of its angles marked as \(x^\circ\) and the other non-right angle marked as \(150^\circ\) exterior to the triangle.
### Description of the Figure:
1. **Right Triangle**: The triangle is a right triangle, indicated by the right angle symbol at the base of the triangle.
2. **Exterior Angle**: The exterior angle adjacent to the base of the triangle is given as \(150^\circ\).
### Explanation of Angles in the Figure:
1. **Straight Line Property**: A straight line forms an angle of \(180^\circ\). The exterior angle of \(150^\circ\) and the interior angle adjacent to it (we'll call it \(y\)) form a straight line together.
Therefore, \(y = 180^\circ - 150^\circ = 30^\circ\).
2. **Sum of Angles in a Triangle**: The sum of the interior angles in a triangle is \(180^\circ\).
Given the right triangle:
- One angle is \(90^\circ\) (the right angle),
- Another angle is \(30^\circ\) (angle \(y\) calculated above),
- The third angle (our angle \(x\)) can be calculated as:
\[
x = 180^\circ - 90^\circ - 30^\circ = 60^\circ
\]
Hence, angle \(x\) measures \(60^\circ\).
### Conclusion:
By applying the properties of angles, we determined that the measure of angle \(x\) is \(60^\circ\).
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