Question

In given fig., $AD=BC$ and $\angle BAD=\angle ABC$, then $\angle ACB$ equals :

• A. $\angle ABD$
• B. $\angle BAD$
• C. $\angle BDA$
• D. $\angle BAC$

Answer 1

Answer: (C)

$\angle BDA$

In $△ADB$ and $△ACB$

$AB=AB$ (common side)

$AD=BC$ (given)

$\angle BAD=\angle ABC$ (given)

$\therefore △ADB\cong ACB$ by $SAS$ congruence rule.

Now corresponding angles of congruent triangles are equal

$\Rightarrow ACB=\angle ADB$