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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q4 (page 197)

$E H = 8 x - 7, F G = 5 x + 11$ In the following figure, a parallelogram $E F G H$ is given and $m ∠ E F G = 70$ . If then find x.

Short Answer

Expert verified

The measure of $x = 6$ .

Step by step solution

01

Step 1. Apply the concept of a parallelogram.

In a parallelogram, the opposite sides are congruent.

02

Step 2. Check the figure.

Consider the figure.

03

Step 3. Step description.

Here $E H = 8 x - 7, F G = 5 x + 11$ .

Since the opposite sides of the parallelogram thus find the value of x as follows:

$\begin{matrix} E H = F G \\ 8 x - 7 = 5 x + 11 \\ 8 x - 5 x = 11 + 7 \\ 3 x = 18 \\ x = 6 \end{matrix}$

Therefore, the measure is $x = 6$ .

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