A) \[30{}^\circ \]
B) \[60{}^\circ \]
C) \[50{}^\circ \]
D) \[180{}^\circ \]
Correct Answer: D
Solution :
\[\Delta ABC\]is isosceles with \[AB=AC\] \[\Rightarrow \]\[\angle BCA=\angle ABC={{50}^{o}}\](Base angles) \[\Rightarrow \]\[\angle BAC={{180}^{o}}-2\times {{50}^{o}}={{80}^{o}}\] \[\angle BDC=\angle BAC={{80}^{o}}\](Angles in the same segment are equal.) BECD is a cyclic quadrilateral in which opposite angles are supplementary. \[\Rightarrow \]\[\angle BEC={{180}^{o}}-\angle BDC\] \[={{180}^{o}}-{{80}^{o}}={{100}^{o}}\] Hence, the required sum \[=BDC+BEC={{80}^{o}}+{{100}^{o}}={{180}^{o}}\]
You need to login to perform this action.
You will be redirected in
3 sec
