Question

In the figure, the value of $x^o$ is ..............

• A. ${80}^o$
• B. ${100}^o$
• C. ${120}^o$
• D. ${200}^o$

Answer 1

The correct option is B ${100}^o$

In given figure, $AB=BC=2$ cm and $AD=CD=3$ cm and Angle $BAD={100}^o$

Join $A$ to $C$

Then in $\Delta ABC,$ $AB=BC=2$ cm

$\therefore \Delta ABC$ is isosceles triangle

$\Rightarrow \angle BAC=ACB$ ...... (1) [Sides opposite to equal angles are equal]

Similarly in $\Delta ADC,AD=CD=3$ cm

$\therefore \Delta ADC$ is an isosceles triangle

$\Rightarrow \angle DAC=ACD$ ....... (2) [Sides opposite to equal angles are equal]

$\angle BAC+\angle DAC=\angle BAD={100}^0$ ...... (Given )

Adding (1) and (2) we get

$\angle BAC+\angle DAC=\angle ACB+\angle ACD$

$\Rightarrow {100}^o=\angle BCD$

$\Rightarrow x^o={100}^o$

Hence, option B is correct.