Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question

What is angle KLM

## 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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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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