Question

In Figure, if congruent right triangles $ABD$ and $DCA$ share leg $\overline{AD}$, then calculate the value of $x$.

• A. ${90}^o$
• B. ${100}^o$
• C. ${110}^o$
• D. ${120}^o$
• E. ${130}^o$

Answer 1

Answer: (D)

In triangle $ABD$,

$\angle$ $ABD$ is $60$ degrees and $\angle$ $BAD$ is $90$ degrees

So, we get angle $ADB$ as $30$ degrees.

Since Both triangles share same leg , we get angle $ABD=ACD=60$
In triangle $ACD$,

$\angle$ $ACD$ is $60$ degrees and $\angle$ $CDA$ is $90$ degrees

So, we get angle $CAD$ as $30$ degrees.
$\Rightarrow x=180-30-30=120$