Question

For what value of x is the figure a rhombus? x=6 x=7.5 x=12 x=18.75

Answer 1

The value of $x$  in the given figure is $\boxed{{\mathbf{12^\circ}}}$  and it matches with $\boxed{{\mathbf{OPTION}}\,\,{\mathbf{C}}}$ .

Further explanation:

A rhombus is shown below in Figure 1.

Now, from Figure 1 it is observed that a rhombus has 4 sides.

A rhombus is a quadrilateral in which opposite sides are equal as well as parallel to each other. In rhombus, all sides are equal; adjacent angles are supplementary to each other.

The property of rhombus is diagonal bisect each other at right angles and diagonal also bisect the angle forming from two sides of rhombus.

In rhombus, diagonals bisect the angles so it is observed from Figure 1, the rhombus angles are equal to each other that is expressed as,

$2x+39=6x-9$

Further simplify the above equation to obtain the value of  $x$ as follows:

$\begin{aligned}2x+39-6x+9&=0\\-4x+48&=0\\x&=\frac{{48}}{4}\\x&=12\\\end{aligned}$

Therefore, the value of $x$  in the given rhombus is $12^\circ$ .

Now, the four options are given below.

$\begin{gathered}{\text{OPTION A}}\to x=6\hfill\\{\text{OPTION B}}\to x=7.5\hfill\\{\text{OPTION C}}\to x=12\hfill\\{\text{OPTION D}}\to x=18.75\hfill\\\end{gathered}$

Since OPTION C matches the obtained value of $x$  that is $12^\circ$ .

Thus, the value of $x$  in the given figure is $\boxed{{\mathbf{12^\circ}}}$  and it matches with $\boxed{{\mathbf{OPTION}}\,\,{\mathbf{C}}}$ .

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Lines and angles

Keywords: angle, regular rhombus, $12$  degree, measure, angle of a rhombus, $2x+39$  , degree, sum of interior angles, $6x-9$ , quadrilateral, $12^\circ$ .

Answer 2

2x+39 = 6x-9

2x = 6x - 48

-4x = -48

x = -48 / -4

x = 12