The inscribed circle I and the edges BC, CA and AB are tangent to the points D, E and F respectively.

∴BF=BD The length of two tangents of a circle drawn from a point outside the circle, etc.

∴∠BDF=∠BFD=( 180？ -∠B)÷2=90？ -? ∠B

CD = CE

∴∠CDE=∠CED=( 180？ -∠C)÷2=90？ -? ∠C

∴∠FDE= 180？ -∠BDF-∠CDE= 180？ -(90? -? ∠B)-(90？ -? ∠C)

=? ∠B+？ ∠C=？ (∠B+∠C)

=? ( 180? -∠A)

=90? -? ∠A