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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: Q13 (page 187)

Quad. STLM is a rhombus.
If $m ∠ 1 = 3 x + 1$ and $m ∠ 3 = 7 x - 11$ find the value of x.

Short Answer

Expert verified

The value of x is 10.

Step by step solution

01

Step 1. Description of step.

Diagonals of a rhombus bisect the vertex angles.

Here, $∠ L S M$ is divided into $∠ 1 and ∠ 2$ , that is, $m ∠ 1 = m ∠ 2$ .

02

Step 2. Description of step.

Here, $∠ S L T$ is divided into $∠ 3 and ∠ 4$ , that is, $m ∠ 3 = m ∠ 4$ .

03

Step 3. Description of step.

Here, $∠ S$ and $∠ L$ are supplementary.

Substitute $m ∠ 3$ for $m ∠ 4$ and $m ∠ 1$ for $m ∠ 2$ to find the value of x.

$\begin{matrix} m ∠ 1 + m ∠ 2 + m ∠ 3 + m ∠ 4 = 180 \\ m ∠ 1 + m ∠ 1 + m ∠ 3 + m ∠ 3 = 180 \\ 2 m ∠ 1 + 2 m ∠ 3 = 180 \\ 2 (m ∠ 1 + m ∠ 3) = 180 \\ 2 (3 x + 1 + 7 x - 11) = 180 \\ 20 (x - 1) = 180 \\ x - 1 = 9 \\ x = 10 \end{matrix}$

Therefore, the value of x is 10.

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