Question

如图,已知△ABC的∠B、∠C的外角平分线交于点D,∠A=80°,求∠D的度数.

Answer 1

∵BD、CD分别∠FBC、∠ECB,

∴∠DBC=1/2∠FBC=1/2(∠A+∠ACB),

∠DCB=1/2∠ECB=1/2(∠ABC+∠A),

∴∠DBC+∠DCB=1/2(∠A+∠ACB+∠ABC+∠A)

=1/2(180°+∠A)

=90°+1/2∠A,

∴∠D=180°-(∠DBC+∠DCB)

=180°-(90°+1/2∠A)

=90°-1/2∠A.