Question

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

$\mathbf{m}\mathbf{\angle }\mathbf{1}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{20}$,$\mathbf{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{x}$

Short answer

The value of$\mathbf{x}$ is 50.

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. Write the relationship between the angles ∠1 and ∠3.

From the given diagram it can be noticed that the angles$\angle 1$ and$\angle 3$ are the angles lying on the same straight line.

Therefore, the sum of the angles$\angle 1$ and$\angle 3$ is $180°$.

That implies, $m\angle 1+m\angle 3=180$.

Step 4. Find the value of x.

As, $m\angle 1+m\angle 3=180$.

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

$\begin{array}{c}m\angle 1+m\angle 3=180\\ m\angle 1+m\angle 2=180\left(\because m\angle 3=m\angle 2\right)\\ 3x-20+x=180\\ 4x-20=180\\ 4x=180+20\\ 4x=200\\ x=\frac{200}{4}\\ x=50\end{array}$

Therefore, the value of$x$ is 50.