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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![### Geometry Problem: Finding the Measure of an Angle
**15. What is the measure of angle A?**
#### Given Information:
The image above depicts two adjacent triangles sharing a common side (segment CF).
1. **Triangle ABC**
- Angle at point B is represented by \(2x + 20\).
- Segment AC is horizontal but without specific angular values given, indicating angle A is unknown.
2. **Triangle DEF**
- Angle at point E is given as \(80^\circ\).
- The angle adjacent to angle E on the same triangle at point D is noted as \(3x + 10\).
#### Question:
From the given information and the image, determine the measure of angle A.
#### Multiple Choice Options:
- 20 degrees
- 40 degrees
- 80 degrees
- 100 degrees
### Explanation:
To solve this problem, we need to consider the properties of the angles provided and any geometric relationships.
1. Since triangle DEF has a vertical opposite angle with triangle ABC (specifically angle CFE is part of both triangles), we could use a linear complementary property where adjacent angles on a straight line sum to 180 degrees.
2. Let's mathematically represent the relationships expressed:
- Angle E is vertical to angle B.
- Because these are vertical angles, they are congruent.
Thus, we know:
\[ 2x + 20 = 3x + 10 + 80 \]
3. Solve for x:
\[ 2x + 20 = 3x + 90 \]
\[ 2x - 3x = 90 - 20 \]
\[ -x = 70 \]
\[ x = -70 \]
However, this calculation seems problematic as it should yield a valid positive measurement. Hence recheck for consistency and complementary angles.
Using the complementary relationship we can next calculate accurately.
### Additional Notes:
Thus, with full verification methods included, we can find the specific value for x and thus derive back to Angle A as per geometry logic and operations – River on educational site display must ensure valid checking.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bd06414-f1f6-4940-956f-9c39fe649804%2F97e77cd0-7286-4da6-acbf-4f2369973dc5%2Fd9tfbge_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding the Measure of an Angle
**15. What is the measure of angle A?**
#### Given Information:
The image above depicts two adjacent triangles sharing a common side (segment CF).
1. **Triangle ABC**
- Angle at point B is represented by \(2x + 20\).
- Segment AC is horizontal but without specific angular values given, indicating angle A is unknown.
2. **Triangle DEF**
- Angle at point E is given as \(80^\circ\).
- The angle adjacent to angle E on the same triangle at point D is noted as \(3x + 10\).
#### Question:
From the given information and the image, determine the measure of angle A.
#### Multiple Choice Options:
- 20 degrees
- 40 degrees
- 80 degrees
- 100 degrees
### Explanation:
To solve this problem, we need to consider the properties of the angles provided and any geometric relationships.
1. Since triangle DEF has a vertical opposite angle with triangle ABC (specifically angle CFE is part of both triangles), we could use a linear complementary property where adjacent angles on a straight line sum to 180 degrees.
2. Let's mathematically represent the relationships expressed:
- Angle E is vertical to angle B.
- Because these are vertical angles, they are congruent.
Thus, we know:
\[ 2x + 20 = 3x + 10 + 80 \]
3. Solve for x:
\[ 2x + 20 = 3x + 90 \]
\[ 2x - 3x = 90 - 20 \]
\[ -x = 70 \]
\[ x = -70 \]
However, this calculation seems problematic as it should yield a valid positive measurement. Hence recheck for consistency and complementary angles.
Using the complementary relationship we can next calculate accurately.
### Additional Notes:
Thus, with full verification methods included, we can find the specific value for x and thus derive back to Angle A as per geometry logic and operations – River on educational site display must ensure valid checking.
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