The problem asks to find the value of $x$ in a pentagon, where four of the angles are given as $68^\circ$, $110^\circ$, $135^\circ$, and $x^\circ$.

1. Problem Description

The problem asks to find the value of $x$ in a pentagon, where four of the angles are given as $68^\circ$, $110^\circ$, $135^\circ$, and $x^\circ$.

2. Solution Steps

The sum of the interior angles of a polygon with $n$ sides is given by the formula:

$S = (n-2) \times 180^\circ$

In this case, the polygon is a pentagon, so $n = 5$.

$S = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$

The sum of the interior angles of the pentagon is $540^\circ$. We are given four angles: $68^\circ$, $110^\circ$, $135^\circ$, and $x^\circ$. Let the fifth angle be $x$. We have:

$68 + 110 + 135 + x = 540$

$313 + x = 540$

$x = 540 - 313$

$x = 227$

3. Final Answer

The value of $x$ is 227.