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
Related questions
Question
explain reasoning
![**3. Angle 'x' in Figure 10.14...Explain your reasoning.**
[Image Description: A geometric figure is shown with two parallel lines. One of the angles formed by the intersecting lines is labeled as 155°. Another angle formed at the bottom right is labeled as 110°. The angle 'x' is located at the top right corner.]
*Figure 10.14: Determine angle x*
**Explanation:**
To determine angle 'x', we need to utilize the properties of parallel lines and the sum of angles around a point. Given that the lines are parallel, we can identify the following relationships:
1. The sum of the angles around a point (on a straight line) is always 180°.
2. Angles on a straight line that are adjacent to each other are supplementary.
First, consider the angle that is supplementary to 155°. This angle, which we will call 'y', is along the same straight line as 155°.
\[ y + 155° = 180° \]
\[ y = 180° - 155° \]
\[ y = 25° \]
Angle 'x' is vertically opposite to angle 'y'. Therefore, angle 'x' is also 25°.
To confirm, observe that the angles around the point where the lines intersect must sum to 360°:
\[ 155° + 25° + 110° + x = 360° \]
Now, solving for 'x':
\[ 155° + 25° + 110° + x = 360° \]
\[ 290° + x = 360° \]
\[ x = 360° - 290° \]
\[ x = 70° \]
Thus, angle 'x' is 70°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c60e9dc-9541-469d-8098-00c54f69ea68%2F05b39860-7445-40b9-9c92-6bd360dbcff4%2Fmw70spr_processed.png&w=3840&q=75)
Transcribed Image Text:**3. Angle 'x' in Figure 10.14...Explain your reasoning.**
[Image Description: A geometric figure is shown with two parallel lines. One of the angles formed by the intersecting lines is labeled as 155°. Another angle formed at the bottom right is labeled as 110°. The angle 'x' is located at the top right corner.]
*Figure 10.14: Determine angle x*
**Explanation:**
To determine angle 'x', we need to utilize the properties of parallel lines and the sum of angles around a point. Given that the lines are parallel, we can identify the following relationships:
1. The sum of the angles around a point (on a straight line) is always 180°.
2. Angles on a straight line that are adjacent to each other are supplementary.
First, consider the angle that is supplementary to 155°. This angle, which we will call 'y', is along the same straight line as 155°.
\[ y + 155° = 180° \]
\[ y = 180° - 155° \]
\[ y = 25° \]
Angle 'x' is vertically opposite to angle 'y'. Therefore, angle 'x' is also 25°.
To confirm, observe that the angles around the point where the lines intersect must sum to 360°:
\[ 155° + 25° + 110° + x = 360° \]
Now, solving for 'x':
\[ 155° + 25° + 110° + x = 360° \]
\[ 290° + x = 360° \]
\[ x = 360° - 290° \]
\[ x = 70° \]
Thus, angle 'x' is 70°.
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