Question

what is the measure of arc BD shown in the diagram below?

Answer 1

we know that
The measure of the external angle is the semi-difference of the arcs that it covers.
so
m∠BCD=(1/2)*[arc AE-arc BD]
20=(1/2)*[85-BD]
40=85-BD
BD=85-40
BD=45°

the answer is
BD=45°

Answer 2

the the measure of arc BD is : 45°