1. **Problem Statement:** Given $\angle MBR = 15^\circ$ and $\angle MBP = 45^\circ$, find $\angle RBP$. 2. **Understanding the problem:** Points $B, P, J, R, M$ lie on a circle with center $U$. We are given two angles at point $B$ involving points $M, R, P$. We need to find the angle $\angle RBP$. 3. **Key rule:** The measure of an angle formed by two chords intersecting on the circle is equal to the sum of the measures of the arcs intercepted by the angle and its vertical angle. Also, the problem hint states: "Measure of an angle is equal to sum of its adjacent angles." 4. **Using the given angles:** - $\angle MBR = 15^\circ$ - $\angle MBP = 45^\circ$ Since $\angle MBP$ includes $\angle MBR$ and $\angle RBP$ (because points $M, R, P$ are on the circle and $B$ is the vertex), we can write: $$\angle MBP = \angle MBR + \angle RBP$$ 5. **Substitute known values:** $$45^\circ = 15^\circ + \angle RBP$$ 6. **Solve for $\angle RBP$:** $$\angle RBP = 45^\circ - 15^\circ = 30^\circ$$ 7. **Final answer:** $$\boxed{30^\circ}$$ This is the measure of $\angle RBP$ correct to two decimal places (30.00°).