9514 1404 393
Answer:
x = 90 degrees
Step-by-step explanation:
There are several ways to go about this (as is often the case with math problems). Here, we'll use the fact that an inscribed angle is half the measure of the arc it intercepts.
arc DE = 2×∠DFE = 60°
arc EF = 2×∠ECF = 60°
arc CF = 2×∠CEF = 60°
Then arc DEC is ...
arc DEC = arc DE +arc EF +arc FC = 60° +60° +60° = 180°
Angle DBC is half the measure of this arc, so is ...
∠DBC = 180°/2 = 90° = x
