Question

In the given figure, the side $BC$ of $△ABC$ has been produced on both the sides; on the left to $D$ and on the right to $E$. If $\angle ABD={96}^o$ and $\angle ACE={130}^o$, find $\angle ABC,\angle ACB$ and $\angle BAC$.

Answer 1

R.E.F image

By linear angle

property,

$\angle 1+96={180}^{\circ }$

$\Rightarrow \angle 1={84}^{\circ }$

Similarly $\angle 2+{130}^{\circ }={180}^{\circ }\Rightarrow \angle 2={50}^{\circ }$

Now as sum of angles in a

triangle $={180}^{\circ },\Rightarrow \angle 1+\angle 2+\angle 3=180$

$\Rightarrow \angle 3=180-134={46}^{\circ }$