Question

in a triangle ABC,AB=AC,BC is produced to D in such a way that AC=CD,triangle BAD=84 degree, triangle BAC =?​

Answer 1

∠BAC  = 52°

Step-by-step explanation:

in a triangle ABC,AB=AC,

=> ∠ABC = ∠ACB = x

∠ABC + ∠ACB + ∠BAC = 180°

=> ∠BAC  = 180° - 2x

in a triangle ACD , AC= CD,

=> ∠CAD = ∠ADC = y

∠CAD + ∠ADC  + ∠ACD = 180°

=> ∠ACD = 180° - 2y

∠ACD = ∠ABC + ∠BAC

=> 180° - 2y = x +  180° - 2x

=> x = 2y

in Δ ABD

x + y   + 84° = 180°

=> x + y = 96°

x = 2y

=> 2y + y = 96°

=> 3y = 96°

=> y = 32°

    x = 64°

∠BAC  = 180° - 2x = 180° - 2(64°)   = 52°

∠BAC  = 52°

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