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 Example: Angles and Intersecting Lines
Consider the diagram shown:
1. **Description:**
- There is a circle with several lines and points labeled around it.
- The points K, L, and M are external to the circle.
- Line LK passes through the circle and extends beyond, intersecting the circumference at two points (not labeled).
- Line KM does not pass through the circle but intersects line LK at point L.
2. **Details:**
- The angle ∠KLM is labeled as 130°.
- There is another angle formed at the intersection point L, between line LM and an unknown angle marked with a question mark (?), which is the angle of interest.
### Analysis:
Assuming the lines form a straight line at point L, which is a supplementary angle scenario:
- The straight line around point L implies that the sum of the angles at a point on a straight line is 180°.
- Given the angle ∠KLM is 130°, the supplementary angle, denoted as ?, can be calculated since these two angles together form a straight line.
### Calculation:
\[ \text{∠KLM} + \text{∠?} = 180^\circ \]
Since ∠KLM is given as 130°,
\[ 130^\circ + \text{∠?} = 180^\circ \]
To find ∠?, we subtract 130° from 180°:
\[ \text{∠?} = 180^\circ - 130^\circ \]
\[ \text{∠?} = 50^\circ \]
**Thus, the unknown angle is 50°.**
### Conclusion:
This diagram illustrates the concept of supplementary angles, where angles on a straight line add up to 180°. This is a fundamental principle in geometry that can be applied to solve various problems involving intersecting lines and angle measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35daa032-30fe-4c4b-94b9-88c0ea4ed82e%2Fff35361b-818c-4d84-a1b4-adee4d3985d2%2F9gqnxh_processed.png&w=3840&q=75)
Transcribed Image Text:## Geometry Example: Angles and Intersecting Lines
Consider the diagram shown:
1. **Description:**
- There is a circle with several lines and points labeled around it.
- The points K, L, and M are external to the circle.
- Line LK passes through the circle and extends beyond, intersecting the circumference at two points (not labeled).
- Line KM does not pass through the circle but intersects line LK at point L.
2. **Details:**
- The angle ∠KLM is labeled as 130°.
- There is another angle formed at the intersection point L, between line LM and an unknown angle marked with a question mark (?), which is the angle of interest.
### Analysis:
Assuming the lines form a straight line at point L, which is a supplementary angle scenario:
- The straight line around point L implies that the sum of the angles at a point on a straight line is 180°.
- Given the angle ∠KLM is 130°, the supplementary angle, denoted as ?, can be calculated since these two angles together form a straight line.
### Calculation:
\[ \text{∠KLM} + \text{∠?} = 180^\circ \]
Since ∠KLM is given as 130°,
\[ 130^\circ + \text{∠?} = 180^\circ \]
To find ∠?, we subtract 130° from 180°:
\[ \text{∠?} = 180^\circ - 130^\circ \]
\[ \text{∠?} = 50^\circ \]
**Thus, the unknown angle is 50°.**
### Conclusion:
This diagram illustrates the concept of supplementary angles, where angles on a straight line add up to 180°. This is a fundamental principle in geometry that can be applied to solve various problems involving intersecting lines and angle measurements.
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