Explanation:
"congruent" in this simple form just means "equally large".
1. angles ISO and JSN, and angles JSO and NSI.
2. therefore, angle ISO = JSN = 113°
angle NSI is complementary to JSN (together they have 180°). NSI = 180 - JSN = 180 - 113 = 67°.
angle JSO = NSI = 67°.
3. yes and yes. they have to be. all inscribed triangles with the baseline being a circle diameter must be congruent. like NJO and NIO.
4. not sure what the yes/no options mean.
related to the angle congruence
arc IN is congruent to JO
arc NJ is congruent to IO
5. the arc angles are the same as the central angles. as this is the definition of the arc angles.
arc angle JO = angle JSO = 67°.
arc angle JN = angle JSN = 113°.
arc angle NI = angle NSI = 67°.
arc angle IO = angle ISO = 113°.
arc angle NJO = angle NO = 180°.
arc angle NIO = angle NO = 180°.
6. therefore, we see,
arc NJO is a half-circle.
arc NIO is a half-circle.
arc JNI is a half-circle.
arc JOI is a half-circle.