A) Less than \[45{}^\circ \]
B) Equal to \[45{}^\circ \]
C) Greater than \[45{}^\circ \]
D) Equal to \[90{}^\circ \]
Correct Answer: A
Solution :
(a): Let angle \[\angle a>45{}^\circ \]: Its complementary angle, say \[\angle b=90-\angle a\,\,\,\,\angle a>45{}^\circ \] \[\therefore \,\,\,\,\,-\angle a<-45{}^\circ \] Add \[90{}^\circ \]to both sides \[\Rightarrow \] \[=\,\,90{}^\circ -\angle a\,\,\,<90{}^\circ -45{}^\circ \] \[\Rightarrow \,\,\angle b\,=90{}^\circ -\angle a<45{}^\circ \] Note: This technique of dealing with inequalities \[\,\angle a>45{}^\circ \Rightarrow \,\,-\,\angle a<-45{}^\circ \] should be learnt and remembered for future applications.
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