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
![### Geometry Problem: Finding the Value of x in a Kite
#### Question 17
**Instructions:**
The figure shown is a kite. Find the value of \( x \).
**Description of the Diagram:**
The diagram represents a kite, a quadrilateral with two distinct pairs of adjacent sides that are equal. The kite has four interior angles marked, with one angle indicated as \( x^\circ \).
- One angle is \( 88^\circ \).
- One angle is \( 35^\circ \).
- The opposite angle of \( x^\circ \) is not provided with a specific measure but can be inferred.
**Steps to solve:**
1. **Understanding Kite Properties:**
- In a kite, the sum of the interior angles of a quadrilateral is always \( 360^\circ \).
- The pairs of adjacent angles at the endpoints of the symmetry axis of the kite are equal.
2. **Calculate the Value of \( x \):**
- Given angles: \( 88^\circ \) and \( 35^\circ \).
- Let \( x \) be the unknown angle.
Since the angles in a kite add up to \( 360^\circ \):
\[
\text{Sum of angles} = 360^\circ
\]
\[
\text{Given angles} = 88^\circ, 35^\circ, 88^\circ \ (\text{since adjacent angles are equal})
\]
\[
\text{Sum of known angles} = 88^\circ + 35^\circ + 88^\circ = 211^\circ
\]
Therefore, the unknown angle \( x \):
\[
x^\circ = 360^\circ - 211^\circ
\]
\[
x = 149^\circ
\]
**Answer:**
\[ x = 149 \text{ degrees} \]
**Input Field:**
\( x = \ \underline{\hspace{3cm}}\ \text{degrees} \)
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Transcribed Image Text:### Geometry Problem: Finding the Value of x in a Kite
#### Question 17
**Instructions:**
The figure shown is a kite. Find the value of \( x \).
**Description of the Diagram:**
The diagram represents a kite, a quadrilateral with two distinct pairs of adjacent sides that are equal. The kite has four interior angles marked, with one angle indicated as \( x^\circ \).
- One angle is \( 88^\circ \).
- One angle is \( 35^\circ \).
- The opposite angle of \( x^\circ \) is not provided with a specific measure but can be inferred.
**Steps to solve:**
1. **Understanding Kite Properties:**
- In a kite, the sum of the interior angles of a quadrilateral is always \( 360^\circ \).
- The pairs of adjacent angles at the endpoints of the symmetry axis of the kite are equal.
2. **Calculate the Value of \( x \):**
- Given angles: \( 88^\circ \) and \( 35^\circ \).
- Let \( x \) be the unknown angle.
Since the angles in a kite add up to \( 360^\circ \):
\[
\text{Sum of angles} = 360^\circ
\]
\[
\text{Given angles} = 88^\circ, 35^\circ, 88^\circ \ (\text{since adjacent angles are equal})
\]
\[
\text{Sum of known angles} = 88^\circ + 35^\circ + 88^\circ = 211^\circ
\]
Therefore, the unknown angle \( x \):
\[
x^\circ = 360^\circ - 211^\circ
\]
\[
x = 149^\circ
\]
**Answer:**
\[ x = 149 \text{ degrees} \]
**Input Field:**
\( x = \ \underline{\hspace{3cm}}\ \text{degrees} \)
**Navigation Buttons:**
- Back
- Next
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