geometry

Question

0

563

2

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

Guest Jun 22, 2020

geno3141 · Answer 1 · 2020-06-22T12:49:31

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

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

Dragan · Answer 2 · 2020-06-25T08:17:51

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

∠ABC+∠CDE = 270º