The problem asks us to write an equation representing the sum of the angles in the given triangle and then solve for the value of $x$. The angles in the triangle are given as $20^{\circ}$, $3x$, and $x$.

1. Problem Description

The problem asks us to write an equation representing the sum of the angles in the given triangle and then solve for the value of $x$. The angles in the triangle are given as $20^{\circ}$, $3x$, and $x$.

2. Solution Steps

The sum of the angles in any triangle is always $180^{\circ}$. Therefore, we can write the equation:

$20 + 3x + x = 180$

Combine the terms with $x$:

$20 + 4x = 180$

Subtract 20 from both sides of the equation:

$4x = 180 - 20$

$4x = 160$

Divide both sides by 4 to solve for $x$:

$x = \frac{160}{4}$

$x = 40$

3. Final Answer

The value of $x$ is 40.