| Direction: In each of the following questions read the given statements and compare the given two quantities on its basis. |
Quantity I. \[x{}^\circ \] Quantity II. \[65{}^\circ \]
A) Quantity I > Quantity II
B) Quantity I \[\ge \] Quantity II
C) Quantity I \[\le \] Quantity II
D) Quantity I < Quantity II
E) No relation between Quantity I and II
Correct Answer: D
Solution :
\[\angle BOC=2\times \angle BAC=2\times 50{}^\circ =100{}^\circ \] As we know, O is the centre of the circle. In \[\Delta BOC,\] \[OB=OC\] \[\angle OBC=\angle OCB\] ?(i) So, \[\angle OBC+\angle OCB=180{}^\circ -100{}^\circ \] From (i), \[2\angle OBC=80{}^\circ \] or, \[\angle OBC=40{}^\circ \] In, \[\Delta BED,\]\[\angle DBE=90{}^\circ -40{}^\circ =50{}^\circ \] Now, \[\angle EBD+\angle EDB+\angle BED=180{}^\circ \] or, \[x{}^\circ =180-(70{}^\circ +50{}^\circ )\] or, \[x{}^\circ =180{}^\circ -120{}^\circ =60{}^\circ \] \[\therefore \]\[x{}^\circ =60{}^\circ \] Hence Quantity I < Quantity II
You need to login to perform this action.
You will be redirected in
3 sec
