We are given a triangle with one exterior angle of $130^\circ$ and one interior angle labeled as $x$. The other interior angle is labeled as $2^\circ$. We need to find the value of $x$.

1. Problem Description

We are given a triangle with one exterior angle of $130^\circ$ and one interior angle labeled as $x$. The other interior angle is labeled as $2^\circ$. We need to find the value of $x$.

2. Solution Steps

First, we find the interior angle adjacent to the $130^\circ$ exterior angle. Since they form a linear pair, their sum is $180^\circ$.

Let the interior angle be $y$.

$y + 130^\circ = 180^\circ$

$y = 180^\circ - 130^\circ$

$y = 50^\circ$

Now we know the three interior angles of the triangle: $x$, $2^\circ$, and $50^\circ$.

The sum of the interior angles of a triangle is $180^\circ$.

$x + 2^\circ + 50^\circ = 180^\circ$

$x + 52^\circ = 180^\circ$

$x = 180^\circ - 52^\circ$

$x = 128^\circ$

3. Final Answer

$x = 128^\circ$