question_answer

In a \[\Delta ABC,\] the altitudes BD and CE are equal and\[\angle A=36{}^\circ .\]What is the value of the\[\angle B\]?

A)  \[72{}^\circ \]

B)  \[84{}^\circ \]

C)  \[18{}^\circ \] 

D)  \[36{}^\circ \]

Correct Answer: A

Solution :

For the \[\Delta BDC\]and \[\Delta BEC\] \[BD=EC,\]\[BC=BC\]and \[\angle BEC=\angle BDC=90{}^\circ \] Thus, \[\Delta BEC\cong \Delta BDC\] \[\therefore \]\[\angle B=\angle C=\frac{180{}^\circ -36{}^\circ }{2}=72{}^\circ \]each