Central angle
Yes.
Angles with the same angle measure are congruent.
has the same measure
45˚
It depends on the angle not all obtuse angles measure the same. To measure an angle you use a protractor.
The angle is 45 degrees.
two angles that have the same angle measure
Congruent angles (or equivalent angles) have the same angle measure.
That depends on the quadrilateral. They will not all have the same measure. Even rectangles will not all have the same central angle measures.
They have the same measure.
It means that all of its sides have the same measure AND all of its angle have the same measure.