The measure of the angle between the internal and external

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The measure of the angle between the internal and external bisectors of an angle is

As per the given in question , we draw a figure of triangle ABC

From figure ,

∠ACF = ∠FCB =		∠C
		2

∠ACE = ∠ECD =		180° - ∠C
		2

∠ACE = 90° -		∠C
		2

∴ ∠FCE = ∠FCA + ∠ACE

∠FCE =		∠C	+ 90° -	∠C	= 90°
		2		2