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

 

 Jan 25, 2021
 #1
avatar+1035 
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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

 Jan 25, 2021
 #2
avatar+116126 
+1

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°

 

 

cool cool cool

 Jan 25, 2021

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