辰 ∠A = ____°.?
D is intersection of [bisector of ∠B and AC].
E is intersection of [bisector of ∠C and AB].
∠ABC : ∠BDE : ∠CED = 2 : 3 : 4.
∠A = ____°.
- IndicaLv 72 years agoFavorite Answer
The angles in the picture are either given or easily deduced.
ED bisects ∠AEC hence AD/DC = EA/EC = sin(6x)/sin(14x)
BD bisects ∠ABC so AD/DC = BA/BC = sin(12x)/sin(14x)
∴ sin(6x) = sin(12x) ⟹ 2sin(6x)cos(9x) = 0 ⟹ x=π/18=10° (only solution since 12x<π)
∠BAC = 40