question_answer

ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If \[\angle DBC=35{}^\circ ,\] then \[\angle AED\]measures [SSC CGL Tier II, 2017]

A) \[35{}^\circ \]

B) \[45{}^\circ \]

C) \[55{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: C

Solution :

[c] In the adjoining figure,                         \[\angle DBC=35{}^\circ \]and \[\angle AED\] its complimentary angle. \[\therefore \]      \[\angle AED+\angle DBC=90{}^\circ \]\[\Rightarrow \]\[\angle AED=55{}^\circ \] \[\Rightarrow \]   \[\angle AED=90{}^\circ -35{}^\circ =55{}^\circ \] \[\Rightarrow \]   \[\angle AED=55{}^\circ \]