figure abcd is a rhombus. what is the value of (x)? - 13 - 14 - 26 - 28

QUESTION IMAGE

Question

figure abcd is a rhombus.
what is the value of (x)?

13
14
26
28

Explanation:

Response

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Identify the geometric relationship

Using the Rhombus Properties knowledge point
In a rhombus, consecutive angles are supplementary because opposite sides are parallel.
\[
m\angle A + m\angle D = 180^\circ
\]

Set up the equation

Using the Rhombus Properties knowledge point
Substitute the given expressions for the angles:
\[
(5x + 25) + (7x - 1) = 180
\]

Solve for x

Using the Solving Linear Equations knowledge point
\[

\begin{aligned} 12x + 24 &= 180\\ 12x &= 156\\ x &= 13 \end{aligned}

\]
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Answer: