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In the figure above, AE is the diameter of the circle.
What is the measure of ∠ABC+∠CDE in degrees?

 

 Jun 22, 2020
 #1
avatar+21953 
0

angle(ABC)  =  ½ ( arc(CD) + arc(DE) + arc(EA) )

angle(CDE)  =  ½ ( arc(EA) + arc(AB) + arc(BC) ),

 

angle(ABC) + angle(CDE  =  ½ ( arc(CD) + arc(DE) + arc(EA) + arc(EA) + arc(AB) + arc(BC) )

 

But arc(EA) = 180o  and  arc(AB) + arc(BC) + arc(CD) + arc(DE) = 180o,

so:  angle(ABC) + angle(CDE  =  ½ ( 180o + 180o + 180o )  =  the answer ...

 Jun 22, 2020
 #2
avatar+1326 
+1

ABCDE is a pentagon with the sum of interior angles of 540º.

 

∠ABC+∠CDE = 270º    indecision

 

 Jun 25, 2020

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