# ABC Is A Triangle In Which Angle B = 2 Angle C. D Is A Point On Side Bc Such That Add Bisectes Angle Bac. And Ab = Cd. Find The Measure Of Angle BAC

Given:

$\angle B = 2 \angle C$

AB = CD

Let

$\angle BAC = 2x$ $\angle BAD = x$ $\angle DAC = x$ $\angle ACD = y$ $\angle ABD = 2y$ $\Rightarrow y – x$ $\angle BAC + \angle ABC + \angle ACD = 180^{\circ}$ $\Rightarrow 2x + 2y + y = 180^{\circ}$ $\Rightarrow 2x + 3y = 180^{\circ}$ $\Rightarrow 2x + 3x = 180^{\circ}$ $\Rightarrow 5x = 180^{\circ}$ $\Rightarrow x = 180^{\circ}/5$ $\Rightarrow x = 36^{\circ}$ $\angle BAC = 2 * 36^{\circ} = 72^{\circ}$

Therefore, the measure of Angle BAC $\angle BAC = 72^{\circ}$

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