Question

In the figure, $\Delta ACB\cong \Delta DCB$, then the value of $x$ and $y$ are:

• A. $14$ cm, ${20}^o$
• B. $28$ cm, ${20}^o$
• C. ${14}^o$, $20$ cm
• D. ${28}^o$, $20$ cm

Answer 1

The correct option is A $14$ cm, ${20}^o$

From the figure, we have,

$\angle D={20}^o,BD=28$ cm.

We need to find value of $x$ and $y$.

In $\Delta ACB\cong \Delta DCB$, we have,

Then the corresponding parts will also be equal.

That is by CPCT rule, corresponding parts of congruent triangles are equal.

Then, $AC=DC$, $CB=CB$, $AB=DB$, $\angle A=\angle D$, $\angle C=\angle C$ and $\angle B=\angle B$.
$\therefore AB=BD$ cm
$\therefore 2x=28$ cm
$\therefore x=14$ cm.

Also, $\angle A=\angle D$
$\therefore y={20}^o$.

Therefore, option $A$ is correct.