1. **Identify circle parts in \( \emptyset O \):**\n\n- Radii: segments from center \( O \) to circle points, e.g., \( OJ \) and \( OS \).\n- Diameters: chords through \( O \) passing entire circle, e.g., \( JS \) and \( MP \).\n- Chords: segments with endpoints on the circle but not through center, e.g., \( JM \) and \( SP \).\n- Minor arcs: smaller arcs between points, e.g., arc \( JS \) and arc \( MP \).\n- Major arcs: larger arcs opposite corresponding minor arcs, e.g., arc \( J\overset{\frown}{S} \) major and arc \( M\overset{\frown}{P} \) major.\n- Semicircles: arcs of exactly 180\degree, e.g., arcs \( J\overset{\frown}{S} \) and \( M\overset{\frown}{P} \) if formed by diameters.\n- Central angles: angles with vertex \( O \), e.g., \( \angle JOC \) and \( \angle SOM \).\n\n2. **Given that \(\angle JOC = 90^\circ\) and segment \( OC \) bisects \( \angle JOC \):**\n\n- Since \( OC \) bisects \(\angle JOC\), it splits it into two equal angles each measuring \( 45^\circ \).\n\n1. \( m\angle JOS = \) Since \( OS \) lies on one side between \( OJ \) and \( OC \), \( m\angle JOS \) corresponds to \( 45^\circ \).\n2. \( m\angle COM = \) Using the circle properties, assuming \( M \) lies such that \( \angle COM \) complements \( \angle JOC \),\n but no direct info, so answer depends on diagram. If \( M \) is on the circumference along \( OP \), and \( OC \) bisects \(\angle JOC\), \( m\angle COM = 45^\circ \).\n3. \( m\angle LOS = \) Without \( L \) given in graphs, insufficient info to determine.\n4. \( m\angle CM = \) Same; unclear without diagram specifics.\n5. \( m\angle CP = \) Likewise, insufficient data.\n6. \( m\angle P = \) Ambiguous; angle with vertex where? Without further info, cannot determine.\n\n**Summary:**\n- Two central angles from bisected right angle measure \( 45^\circ \) each: \( m\angle JOS = m\angle COM = 45^\circ \).\n- Other measures require more info or diagram data.\n\n