geometry

Pentagon ABCDE is inscribed in a circle with a center at O and diameter AB. Find the measure of angle AED + angle DCB in degrees.

∠AED + ∠DCB = 270 degrees

Angle AED's  sum of its intercepted arcs  =    AB  +  BC +  DC

Angle DCB's  sum of its intercepted arcs =  ED + AE  +  AB

So ,  combined,  they intercept  arcs of    2AB  + AE  + ED +  DC  +  BC

2AB   = 360°  

AE + ED + DC  + BC  =  180°

So   their combined measures =  (1/2) ( 360 + 180)  =  (1/2) (540)  = 270°