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Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q28 (page 170)

$鈻� DECK$ is a parallelogram. Complete.
If $m 鈭� 1 = 42, m 鈭� 2 = x^{2}$ and $m 鈭� CED = 13 x$ then $m 鈭� 2 = ?$ or $m 鈭� 2 = ?$ (numerical answers).

Short Answer

Expert verified

The value of $m 鈭� 2$ is $36 掳$ or $49 掳$ .

Step by step solution

01

Step 1. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $鈭� K$ and $鈭� E$ are opposite angles, such that,

$\begin{matrix} m 鈭� 1 + m 鈭� 2 = m 鈭� C E D \\ 42 + x^{2} = 13 x \\ x^{2} 鈭� 13 x + 42 = 0 \end{matrix}$

02

Step 2. Solve the quadratic equation.

Solve the obtained quadratic equation in step 1 to find the value of x.

$\begin{array}{l} x^{2} 鈭� 13 x + 42 = 0 \\ x^{2} 鈭� 6 x 鈭� 7 x + 42 = 0 \\ x (x 鈭� 6) 鈭� 7 (x 鈭� 6) = 0 \\ x 鈭� 6 = 0 or x 鈭� 7 = 0 \\ x = 6 orx = 7 \end{array}$

Solving equation $x^{2} 鈭� 3 x 鈭� 70 = 0$ gives the roots as, $x = 6 or x = 7$ .

03

Step 3. Description of step.

Substitute 6 for x into $m 鈭� 2 = x^{2}$ to find the value of $m 鈭� 2$ .

$\begin{matrix} m 鈭� 2 = x^{2} \\ = 6^{2} \\ = 36 掳 \end{matrix}$

04

Step 4. Description of step.

Substitute 7 for x into $m 鈭� 2 = x^{2}$ to find the value of $m 鈭� 2$ .

$\begin{matrix} m 鈭� 2 = x^{2} \\ = 7^{2} \\ = 49 掳 \end{matrix}$

Therefore, the value of $m 鈭� 2$ is $36 掳$ or $49 掳$ .

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