If quadrilateral ABCD is an isosceles trapezoid, find x. D. 65 (7x - 26)"

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
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### Solving for x in an Isosceles Trapezoid

**Problem Statement:**
If quadrilateral ABCD is an isosceles trapezoid, find \( x \).

**Diagram:**
Here is a representation of quadrilateral ABCD, which is an isosceles trapezoid:

```
      A ____________ D
     /                       \
    /                         \
 B/_________________\ C
```

- \(\angle B = 65^\circ\)
- \(\angle C = (7x - 26)^\circ\)

**Description:**

In the given quadrilateral ABCD, which is an isosceles trapezoid, we have the following angles:

- \(\angle B = 65^\circ\) is given.
- \(\angle C = (7x - 26)^\circ\) is given in terms of x.

**To Solve for \( x \):**
1. In an isosceles trapezoid, the angles on the same base are supplementary, meaning:
   
   \[
   \angle B + \angle C = 180^\circ
   \]
   
2. Substituting the given angles into the equation:
   
   \[
   65^\circ + (7x - 26)^\circ = 180^\circ
   \]
   
3. Simplify and solve for \( x \):
   
   \[
   65 + 7x - 26 = 180
   \]
   \[
   7x + 39 = 180
   \]
   \[
   7x = 141
   \]
   \[
   x = \frac{141}{7}
   \]
   \[
   x = 20.14
   \]

**Answer:**
\( x = 20.14 \)

**Interactive Tools:**
- Calculator interface with number and operation buttons available for solving equations.
- Additional tools for zooming, bookmarking, highlighting, using a line reader, and resetting answers.

This exercise helps in understanding the properties of trapezoids, particularly focusing on the supplementary angles in isosceles trapezoids.
Transcribed Image Text:### Solving for x in an Isosceles Trapezoid **Problem Statement:** If quadrilateral ABCD is an isosceles trapezoid, find \( x \). **Diagram:** Here is a representation of quadrilateral ABCD, which is an isosceles trapezoid: ``` A ____________ D / \ / \ B/_________________\ C ``` - \(\angle B = 65^\circ\) - \(\angle C = (7x - 26)^\circ\) **Description:** In the given quadrilateral ABCD, which is an isosceles trapezoid, we have the following angles: - \(\angle B = 65^\circ\) is given. - \(\angle C = (7x - 26)^\circ\) is given in terms of x. **To Solve for \( x \):** 1. In an isosceles trapezoid, the angles on the same base are supplementary, meaning: \[ \angle B + \angle C = 180^\circ \] 2. Substituting the given angles into the equation: \[ 65^\circ + (7x - 26)^\circ = 180^\circ \] 3. Simplify and solve for \( x \): \[ 65 + 7x - 26 = 180 \] \[ 7x + 39 = 180 \] \[ 7x = 141 \] \[ x = \frac{141}{7} \] \[ x = 20.14 \] **Answer:** \( x = 20.14 \) **Interactive Tools:** - Calculator interface with number and operation buttons available for solving equations. - Additional tools for zooming, bookmarking, highlighting, using a line reader, and resetting answers. This exercise helps in understanding the properties of trapezoids, particularly focusing on the supplementary angles in isosceles trapezoids.
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