Question

What is the measure of the inscribed angle that shares endpoints with a central angle measuring 58 degrees?

Answer 1

29 degrees

Explanation:

See attached image of an inscribed angle together with a central angle.

An inscribed angle is half the measure of the central angle! Always! In my image, if the measure of angle CAB is 58 degrees, then that is also the measure of arc CB. The inscribed angle CDB is half the measure of the intercepted arc CB, so it's 29 degrees.