Question

如图,在△ABC中,∠B,∠C的平分线交于点O.(1)若∠A=50°,求∠BOC的度数;

Answer 1

先推导公式,其它问题都可解决：

∵OB、OC分别平分∠ABC、∠ACB,

∴∠OBC=1/2∠ABC,∠OCB=1/2∠ACB,

∴∠O=180°-(∠OBC+∠OCB)

=180°-1/2(∠ABC+∠ACB)

=180°-1/2(180°-∠A)

=90°+1/2∠A.

⑴∠O=90°+1/2×50°=115°,

⑵∠O=90°-1/2n°.

⑶∠O=3∠A,

90°+1/2∠A=3∠A,

∠A=36°.