A) \[\text{45 }\!\!{}^\circ\!\!\text{ }\]
B) \[65{}^\circ \]
C) \[\text{85 }\!\!{}^\circ\!\!\text{ }\]
D) \[\text{90 }\!\!{}^\circ\!\!\text{ }\]
Correct Answer: B
Solution :
In\[\Delta \text{PQS}\], we have \[\angle PSQ=180{}^\circ -(100{}^\circ +40{}^\circ )=180{}^\circ -140{}^\circ =40{}^\circ \]Also, \[\angle PSR=85{}^\circ \] or \[40{}^\circ +\angle QSR=85{}^\circ \] \[\therefore \angle QSR=85{}^\circ -40{}^\circ =45{}^\circ \] A s \[\text{SQ }\!\!|\!\!\text{ }\!\!|\!\!\text{ RT}\] \[\therefore \angle QSR=\angle TRU=45{}^\circ \] (corresponding angles) So, \[\angle QRT=180{}^\circ -(70{}^\circ +45{}^\circ )\] (linear pair) \[=180{}^\circ -115{}^\circ =65{}^\circ \]You need to login to perform this action.
You will be redirected in
3 sec