Geometry. what is the measure of de?

68



Explanation:

Segment EC is a diameter as it goes through the circle center point O. So arc EDC is 180 degrees in measure.

Arc EDC is composed of the minor arcs DE and DC. 
In other words, the two minor arcs mentioned add up to 180 degrees
We want to know DE and we know that DC = 112

So,
(minor arc DE) + (minor arc DC) = arc EDC
(minor arc DE) + (minor arc DC) = 180
(minor arc DE) + (112) = 180
(minor arc DE) + 112 - 112 = 180 - 112
minor arc DE = 68