Question

Please send me the answer .

Answer 1

Note:  It should be AD bisects BAC.

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From figure:

Given, ∠BDA = 70°.

⇒ ∠BDA + ∠ADC = 180°

⇒ 70° + ∠ADC = 180°

⇒ ∠ADC = 110°.

Given that  AD = DC.

So, ∠DAC = ∠ACD.   ----- (i)

Now,

⇒ ∠ADC + ∠DAC + ∠ACD = 180°.

⇒ 110° + ∠ACD + ∠ACD = 180°

⇒ 110° + 2∠ACD = 180°

⇒ 2∠ACD = 180° - 110°

⇒ 2∠ACD = 70°.

⇒ ∠ACD = 35°.

So, ∠DAC = ∠ACD = ∠DAB = 35°.

Now,

We know that sum of angles of a triangle is 180°.

⇒ ∠DAB + ∠ABD + ∠BDA = 180°

⇒ 35 + ∠ABD + 70° = 180°

⇒ ∠ABD + 105° = 180°

⇒ ∠ABD = 180° - 105°

⇒ ∠ABD = 75°.

Therefore, ∠ABD = 75°.

Hope this helps!