In triangle \( \triangle JRW \), the sum of the angles must equal 180 degrees. You have the measures of angle \( J \) and angle \( W \):
- \( m\angle J = 47^\circ \)
- \( m\angle W = 15^\circ \)
To find the measure of angle \( R \) (denoted as \( m\angle R \)), we can use the following formula:
\[ m\angle R = 180^\circ - (m\angle J + m\angle W) \]
Now, substituting the known angles:
\[ m\angle R = 180^\circ - (47^\circ + 15^\circ) \] \[ m\angle R = 180^\circ - 62^\circ \] \[ m\angle R = 118^\circ \]
Thus, the measure of angle \( R \) is:
\[ \boxed{118^\circ} \]