Question

Quad. SLTM is a rhombus.

If$\mathbf{m}\angle \mathbf{1}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{8}$ and$\mathbf{m}\angle \mathbf{2}\mathbf{=}\mathbf{11}\mathbf{x}\mathbf{-}\mathbf{24}$ find the value of x.

Short answer

The value of x is 4.

Step-by-step solution

Step 1. Description of step.

Diagonals of a rhombus bisect the vertex angles.

Here, $\angle LSM$is divided into $\angle 1\text{and}\angle \text{2}$, that is, $m\angle 1=m\angle 2$.

Step 2. Description of step.

Substitute $3x+8$for $m\angle 1$and $11x-24$into $m\angle 1=m\angle 2$.

$\begin{array}{c}3x+8=11x-24\\ 11x-3x=24+8\\ 8x=32\end{array}$

Step 3. Description of step.

Divide each side of the obtained equation in steps 2 by 8 to find the value of x.

$\begin{array}{c}\frac{8x}{8}=\frac{32}{8}\\ x=4\end{array}$

Therefore, the value of x is 4.