question_answer

In\[\Delta \,ABC\], \[\angle B=\text{ }60{}^\circ ,\]\[\angle C=40{}^\circ .\] If AD bisects  \[\angle BAC\]and AE \[\bot \] BC, then \[\angle EAD\]is

A) \[10{}^\circ \]                          

B)  \[20{}^\circ ~\]

C) \[40{}^\circ \]                          

D)  \[80{}^\circ ~\]

Correct Answer: A

Solution :

         \[\angle B=60{}^\circ ;\text{ }\angle C=40{}^\circ \] \[\angle A=180-100=80{}^\circ \]             \[\angle BAD=\angle DAC=40{}^\circ \] \[\therefore \] From \[\Delta \]ABE, \[\angle BAE=180{}^\circ -60{}^\circ -90{}^\circ =30{}^\circ \] =\[30{}^\circ \] \[\angle EAD=40-30=10{}^\circ \]