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70. Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the figure. If 80° C

70. Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the figure. If 80° C

Elementary Geometry For College Students, 7e
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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determine angle x ans y of picnic table with know 80 degree angle 

### Example Problem for Educational Purposes: Determining Angles **Problem Statement:** Given that \( m \angle ABC = 80^\circ \), determine \( m \angle x \) and \( m \angle y \) so that the top of the table will be parallel to the ground. **Explanation:** In this problem, you are given an angle \( \angle ABC \) with a measure of \( 80^\circ \). To find the measures of angles \( x \) and \( y \), additional information or context about their relationships with angle \( ABC \) and each other is needed. - \( m \angle ABC \): the given angle with a measure of \( 80^\circ \). - \( \angle x \) and \( \angle y \): the angles we need to determine to ensure that a certain condition (the table being parallel to the ground) is met. To solve the problem, we typically need to know the geometric configuration involving these angles, such as whether they are part of a larger shape (e.g., triangle, rectangle) or if specific relationships (e.g., supplementary, complementary) are provided. When the problem involves making a surface parallel to the ground, we might consider concepts like corresponding angles (if there are parallel lines involved) and the properties of parallel lines intersected by a transversal. **Note:** Since the image only provides a partial view, and hence limited context, ensure to review the complete problem statement and diagrams (if any) provided in your textbook or resource material to solve the problem accurately.
Transcribed Image Text:### Example Problem for Educational Purposes: Determining Angles **Problem Statement:** Given that \( m \angle ABC = 80^\circ \), determine \( m \angle x \) and \( m \angle y \) so that the top of the table will be parallel to the ground. **Explanation:** In this problem, you are given an angle \( \angle ABC \) with a measure of \( 80^\circ \). To find the measures of angles \( x \) and \( y \), additional information or context about their relationships with angle \( ABC \) and each other is needed. - \( m \angle ABC \): the given angle with a measure of \( 80^\circ \). - \( \angle x \) and \( \angle y \): the angles we need to determine to ensure that a certain condition (the table being parallel to the ground) is met. To solve the problem, we typically need to know the geometric configuration involving these angles, such as whether they are part of a larger shape (e.g., triangle, rectangle) or if specific relationships (e.g., supplementary, complementary) are provided. When the problem involves making a surface parallel to the ground, we might consider concepts like corresponding angles (if there are parallel lines involved) and the properties of parallel lines intersected by a transversal. **Note:** Since the image only provides a partial view, and hence limited context, ensure to review the complete problem statement and diagrams (if any) provided in your textbook or resource material to solve the problem accurately.
### Angles on a Picnic Table #### Problem Statement: The legs of a picnic table form an isosceles triangle as indicated in the figure. The angle at the bottom of the isosceles triangle (∠BAC) measures 80°. The goal is to determine the measures of the other two angles x and y. #### Diagram Description: - There is a square picnic tabletop represented at the top of the diagram. - Below the tabletop, there are two legs represented as intersecting lines that form an "X" shape. - The intersection of the legs below the tabletop forms an isosceles triangle with vertices labeled A, B, and C, where ∠BAC = 80°. - The angles at the top of the legs where they meet the tabletop are labeled as x and y respectively. ##### Analysis: Given that the triangle is isosceles and the angle between the two equal legs (at A) is 80°, you can find the measures of the other angles as follows: Since the sum of angles in any triangle is 180°: \[ ∠BAC + ∠BCA + ∠B = 180° \] \[ 80° + x + x = 180° \] \[ 80° + 2x = 180° \] \[ 2x = 100° \] \[ x = 50° \] So, the angles x and y (∠B and ∠C) are both 50° each. Thus, the angles of the isosceles triangle formed by the picnic table legs are: - ∠BAC = 80° - ∠B = 50° - ∠C = 50° This decomposition helps in practical applications such as design and load analysis in construction and engineering fields.
Transcribed Image Text:### Angles on a Picnic Table #### Problem Statement: The legs of a picnic table form an isosceles triangle as indicated in the figure. The angle at the bottom of the isosceles triangle (∠BAC) measures 80°. The goal is to determine the measures of the other two angles x and y. #### Diagram Description: - There is a square picnic tabletop represented at the top of the diagram. - Below the tabletop, there are two legs represented as intersecting lines that form an "X" shape. - The intersection of the legs below the tabletop forms an isosceles triangle with vertices labeled A, B, and C, where ∠BAC = 80°. - The angles at the top of the legs where they meet the tabletop are labeled as x and y respectively. ##### Analysis: Given that the triangle is isosceles and the angle between the two equal legs (at A) is 80°, you can find the measures of the other angles as follows: Since the sum of angles in any triangle is 180°: \[ ∠BAC + ∠BCA + ∠B = 180° \] \[ 80° + x + x = 180° \] \[ 80° + 2x = 180° \] \[ 2x = 100° \] \[ x = 50° \] So, the angles x and y (∠B and ∠C) are both 50° each. Thus, the angles of the isosceles triangle formed by the picnic table legs are: - ∠BAC = 80° - ∠B = 50° - ∠C = 50° This decomposition helps in practical applications such as design and load analysis in construction and engineering fields.
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