Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-35

In \[\Delta ABC,\]\[\angle A:\angle B:\angle C=2:3:4,\] a line CD drawn perpendicular to AB, then \[\angle ACD\] is            [SSC (CGL) 2013]

A) \[80{}^\circ \]

B) \[20{}^\circ \]

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

D) \[60{}^\circ \]

Correct Answer: C

Solution :

Let the angles be \[2x,\]\[3x\]and\[4x.\]

Since, the sum of interior angles of triangle is \[180{}^\circ .\]

Then, \[2x+3x+4x=180{}^\circ \]

\[\Rightarrow \] \[9x=180{}^\circ \]

\[\therefore \] \[x=20{}^\circ \]

Now, \[\angle A=2x=2\times 20{}^\circ =40{}^\circ \]

\[\angle B=3x=3\times 20{}^\circ =60{}^\circ \]

\[\angle C=4x=4\times 20{}^\circ =80{}^\circ \]

Now, \[AB\bot CD\]and AC be the transversal.

Then, \[\angle BCD=\angle ACD\][alternate interior angles]

\[\therefore \] \[\angle ACD=40{}^\circ \]