To find the measure of angle m, we can use a property of circles that states that the measure of an angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.
Since RU is tangent to the circle at R, we know that angle m is formed by the tangent and chord US. Therefore, the measure of angle m is equal to half the measure of the intercepted arc RS.
Given that mRS = 84°, we know that the intercepted arc RS is 2 * 84° = 168°.
Therefore, the measure of angle m is half of 168°, which is 84°.
m = 84° (since tangent lines to a circle are perpendicular to the radius at the point of tangency).
