Because: Be and CF are bisectors of ∠ABC and ∠ACB, respectively.

So:

∠ABE=∠CBE=( 1/2)∠ABC

∠ACF=∠BCF=( 1/2)∠ACB

1)

So:

∠BGC= 180 -∠CBE-∠BCF

∠BGC = 180-( 1/2)∠ ABC -( 1/2)∠ACB

So:

∠BGC = 180-( 1/2)(∠ABC+∠ACB)

2)

Because: ∠ ABC+∠ ACB = 180-∠ A

Substitute 1) to know:

∠BGC = 180-( 1/2)( 180-∠A)

∠BGC=90 +( 1/2)∠A