Rotating a triangle on a coordinate plane affects the orientation and position of the triangle, but it does not change the measures of its angles. Since a rotation is a rigid transformation, it preserves angles and lengths. Therefore, the measure of each angle in the triangle remains unchanged after the rotation.

If the original triangle's angles were, for example, $x^\circ$, $y^\circ$, and $z^\circ$, they would remain $x^\circ$, $y^\circ$, and $z^\circ$ after a 90-degree clockwise rotation.

With this understanding, the problem does not provide enough information to directly determine the measure of the third angle from the given choices (A: $82^\circ$, B: $98^\circ$, C: $53^\circ$, D: $45^\circ$) without knowing the measures of the other two angles in the triangle.

In summary, to find the measure of the third angle, we would need the measures of the other two angles in the triangle. The sum of all three angles in a triangle is always $180^\circ$.