A) \[{{20}^{o}}\]
B) \[{{10}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{40}^{o}}\]
Correct Answer: C
Solution :
Given, \[\angle PQR={{120}^{o}}\] \[\therefore \]Reflex \[\angle POR=2\angle PQR=2({{120}^{o}})={{240}^{o}}\] Now, \[\angle POR={{360}^{o}}-\text{Relex}\,\angle POR\] \[={{360}^{o}}-{{240}^{o}}={{120}^{o}}\] ?(i) Also, \[OP=OR\Rightarrow \angle OPR=\angle ORP\] ?(ii) (Angles opposite to equal sides of a triangle are equal) In \[\Delta OPR+\angle OPR+\angle ORP+\angle POR={{180}^{o}}\] \[\Rightarrow \]\[2\angle OPR+{{120}^{o}}={{180}^{o}}\][From (i) & (ii)] \[\Rightarrow \]\[2\angle OPR={{60}^{o}}\Rightarrow \angle OPR={{30}^{o}}\]
You need to login to perform this action.
You will be redirected in
3 sec
