Question

In the given figure, $\Delta$ABC is an isosceles triangle with AB$=$AC and $\angle$ABC$={50}^o$. Find $\angle$BDC and $\angle$BEC respectively.

• A. ${100}^o,{60}^o$
• B. ${50}^o,{120}^o$
• C. ${60}^o,{80}^o$
• D. ${80}^o,{100}^o$

Answer 1

The correct option is D ${80}^o,{100}^o$

$△ABC$ is an isosceles triangle.

$\therefore \angle B=\angle C={50}^o$

$\angle BAC=180-50-50={80}^o$

$\angle BAC=\angle BDC={80}^o$ (angles on circle by the same chord on the same segment are equal)

$\angle BEC$ is supplementary angle of $\angle BAC$

$\therefore \angle BEC=180-\angle BAC=180-80={100}^o$