Circles SAT question

The correct answer is $46$. It's given that $O$ is the center of a circle and that points $R$ and $S$ lie on the circle. Therefore, $\overline{\mathrm{OR}}$ and $\overline{\mathrm{OS}}$ are radii of the circle. It follows that $OR=OS$. If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles $\angle RSO$ and $\angle ORS$, which are across from the sides of equal length, are congruent. Let $x^{\circ }$ represent the measure of $\angle RSO$. It follows that the measure of $\angle ORS$ is also $x^{\circ }$. It's given that the measure of $\angle ROS$ is $88^{\circ }$. Because the sum of the measures of the interior angles of a triangle is $180^{\circ }$, the equation $x^{\circ }+x^{\circ }+88^{\circ }=180^{\circ }$, or $2x+88=180$, can be used to find the measure of $\angle RSO$. Subtracting $88$ from both sides of this equation yields $2x=92$. Dividing both sides of this equation by $2$ yields $x=46$. Therefore, the measure of $\angle RSO$, in degrees, is $46$.