We are given a circle with center O. We are given the angle POR is $56^\circ$. We are asked to find the value of $x$ where the angle PQR is $2x$.

1. Problem Description

We are given a circle with center O. We are given the angle POR is $56^\circ$. We are asked to find the value of $x$ where the angle PQR is $2x$.

2. Solution Steps

The angle at the center of a circle subtended by an arc is twice the angle at the circumference subtended by the same arc.

In this case, angle POR is at the center, and angle PQR is at the circumference. Therefore,

$POR = 2 \times PQR$

$56^\circ = 2 \times 2x$

$56 = 4x$

$x = \frac{56}{4}$

$x = 14$

3. Final Answer

The value of $x$ is 14.