In the circle shown below segment BD is a diameter and the measure of arc CB is 36; what is the measure of angle DBC?

To find the measure of angle DBC, we can use the property that an angle inscribed in a circle is half the measure of the arc it subtends.

In this case, segment BD is a diameter. Since arc CB measures 36 degrees, angle DBC (which subtends arc CB) is calculated as follows:

Angle DBC = (Measure of arc CB) / 2

Substituting the given measure of arc CB:

Angle DBC = 36 degrees / 2 = 18 degrees

Thus, the measure of angle DBC is 18 degrees.