Question

In the given $\Delta ABC$ (as shown in fig.) DE is parallel to BC and BE bisects $\angle DEC$. If $\angle C={80}^o$, find the value of x.

• A. ${50}^o$
• B. ${80}^o$
• C. ${75}^o$
• D. ${30}^o$

Answer 1

Answer: (A)

${50}^o$

Given that in triangle $ABC,DE$ is parallel to $BC$ and $BE$ bisects $\angle DEC$ and $\angle C={80}^0$.

Given $DE\parallel BC$ and line BE join both parallel line

$\therefore \angle DEB=\angle EBC=x$ ...... ( Transversal angle)

$\angle DEB=\angle CEB$ ...... (given)

$\angle CEB=\angle EBC=x$

In $\Delta BEC,$

$x+x+80=180\Rightarrow 2x=180-80=100$

$\Rightarrow x={50}^0$