question_answer

\[\Delta ABC\] is right - angled at B. If the measures of \[\angle A\] and \[\angle C\] are in the ratio \[7:5\] then what is the measure of \[\angle C\]?

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

B)  \[60{}^\circ \]

C)  \[37.5{}^\circ \]           

D)  \[70{}^\circ \]

Correct Answer: C

Solution :

(c): \[\angle A+\angle C=90{}^\circ :\]Now, let \[\angle A=7x;\] \[\angle C=5x\] Then,  \[7x+5x=90{}^\circ \]                 \[\Rightarrow \,\,x=\frac{90{}^\circ }{12}=7.5{}^\circ \,\,\,\therefore \,\,\,\angle C=5x=37.5{}^\circ \]