Question

The side BC of a $△ABC$ is produced upto D If $\angle ACD=8\angle BAC$ and AB=AC then the value of $\angle BAC$ is

• A. ${12}^{\circ }$
• B. ${13}^{\circ }$
• C. ${14}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is A ${12}^{\circ }$

Given side BC of a △ABC is produced upto D If ∠ACD=8∠BAC

Then in $\Delta ABC$ AB=AC then $\angle ABC=\angle ACB$ And $\angle ABC+\angle ACB+\angle BAC={180}^0$

So $\angle ACB=\frac{180-\angle ABC}{2}$

the side BC produced up toD

The BCD id streaite line

Then $\angle ACB+ACD=180$ we know that $\angle ACB=\frac{180-\angle ABC}{2}$ and given $\angle ACD=8\angle ABC$

$\therefore \frac{180-\angle ABC}{2}+8\angle ABC=180$

$\Rightarrow 15\angle ABC=180$

$\Rightarrow \angle ABC={12}^0$