Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 years ago

辰 ∠A = ____°.?

Triangle ABC.

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 = ____°.

1 Answer

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  • Indica
    Lv 7
    2 years ago
    Favorite 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

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