證明：∵?$BI、$??$CI$?分別平分?$∠ABC、$??$∠ACB$?
∴?$∠IBC=\frac {1} {2}∠ABC，$??$∠ICB=\frac {1} {2}∠ACB$?
∵?$∠A+∠ABC+∠ACB=180°$?
∴?$∠ABC+∠ACB=180°-∠A$?
∵?$∠BIC+∠IBC+∠ICB=180°$?
∴?$∠BIC=180°-(∠IBC+∠ICB)$?
?$ =180°-\frac {1} {2}(∠ABC+∠ACB)$?
?$ =180°-\frac {1} {2}(180°-∠A)$?
?$ =90°+\frac {1} {2}∠A$?
