a) To find angle x:

Here's how to find the values of angles $x$, $y$, and $m$:

a) To find angle $x$: Angle $x$ is $\angle POQ$. Step 1: Identify the type of triangle $\triangle OPQ$. Since $O$ is the center of the circle, $OP$ and $OQ$ are both radii. Therefore, $\triangle OPQ$ is an isosceles triangle with $OP = OQ$.

Step 2: Determine the base angles of $\triangle OPQ$. In an isosceles triangle, the angles opposite the equal sides are equal. So, $\angle OQP = \angle OPQ$. Given $\angle OPQ = 24^\circ$, thus $\angle OQP = 24