We are given a circle with center P. An angle $x$ at the center P and an inscribed angle of $148^\circ$ are shown. We are asked to find the value of $x$. The sum of angles around a point is $360^\circ$.

1. Problem Description

We are given a circle with center P. An angle $x$ at the center P and an inscribed angle of $148^\circ$ are shown. We are asked to find the value of $x$. The sum of angles around a point is $360^\circ$.

2. Solution Steps

The sum of the angles around the center of a circle is $360^\circ$.

We have two angles at the center of the circle: $x$ and the angle corresponding to the arc where the inscribed angle is. The inscribed angle is $148^\circ$. The central angle corresponding to the same arc is twice the inscribed angle. Let this central angle be $y$. Therefore,

$y = 2 \times 148^\circ = 296^\circ$.

We know that the sum of the angles around point P is $360^\circ$.

So, $x + y = 360^\circ$.

Substituting the value of $y$, we have $x + 296^\circ = 360^\circ$.

$x = 360^\circ - 296^\circ$.

$x = 64^\circ$.

3. Final Answer

$x = 64$