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:

[latex] \angle B = 2 \angle C [/latex]

AB = CD

Let

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

Therefore, the measure of Angle BAC [latex] \angle BAC = 72^{\circ} [/latex]

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