Question

In the figure, $\angle BCD=\angle ADC$ and $\angle ACB=\angle BDA$.

• A. $\angle B=\angle B$
• B. $\angle A=\angle D$
• C. $\angle A=\angle B$
• D. $\angle C=\angle D$

Answer 1

Answer: (C)

$\angle A=\angle B$

In $△ACD$ and $△BDC$

$\angle BCD=\angle ADC$ [Given].

Given,$\angle ACB=\angle BDA$.

Adding these two above equation , we get,

$\angle BCD+\angle ACB=\angle ADC+\angle BDA$

$⟹$ $\angle ACD=\angle BDC$.

Also, $CD=CD$ [Common]

$△ACD\cong △BDC$ .....(By $ASA$ congruency criterion).

Therefore, by $CPCT$ rule, the corresponding parts are equal.

Then, $AD=BC$ and $\angle A=\angle B$.

Hence, option $C$ is correct.