question_answer

In \[\Delta ABC,\] \[\angle A=x{}^\circ ,\] \[\angle B=(3x-2){}^\circ ,\] \[\angle C=y{}^\circ ,\]also then is

A)  \[32{}^\circ \] 

B)  \[73{}^\circ \]

C)  \[25{}^\circ \]

D)  \[78{}^\circ \]

Correct Answer: B

Solution :

\[\because \]\[\angle A+\angle B+\angle C=180{}^\circ \]

\[x+(3x-2)+y=180{}^\circ ;4x+y=182\]?(i)

Also,     \[\angle C-\angle B=9{}^\circ \]

\[y-(3x-2)=9{}^\circ \]

\[y-3x=7{}^\circ \]                                ?(ii)

On subtracting Eq. (ii) from Eq. (i), we get

\[\angle B=\,\,(3x-2)=3\times 25{}^\circ -2=73{}^\circ \]