Question

Find the value of $\mathbf{x}$.

$\mathbf{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{12}$,$\mathbf{m}\mathbf{\angle }\mathbf{3}\mathbf{=}\mathbf{4}\left(x-7\right)$

Short answer

The value of$x$ is 20.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the relationship between the angles ∠2 and ∠3.

From the given diagram it can be noticed that the angles$\angle 2$ and$\angle 3$ are the corresponding angles.

Therefore, the measures of the angles$\angle 2$ and$\angle 3$ are equal.

That implies, $m\angle 2=m\angle 3$.

Step 3. Find the value of x.

As, $m\angle 2=m\angle 3$.

Therefore, the value of$x$ is given by:

$\begin{array}{c}m\angle 2=m\angle 3\\ 2x+12=4\left(x-7\right)\\ 2x+12=4x-28\\ 12+28=4x-2x\\ 40=2x\\ \frac{40}{2}=x\\ 20=x\end{array}$

Therefore, the value of$x$ is 20.