question_answer

ABCD is a square, P, Q, R and 5 are points on the sides AB, BC, CD and DA, respectively such that AP = BQ = CR = DS. What is the value of\[\angle SPQ\]?

A)  \[30{}^\circ \] 

B)  \[45{}^\circ \]

C)  \[60{}^\circ \] 

D)  \[90{}^\circ \]

Correct Answer: D

Solution :

In \[\Delta APS\]and \[\Delta PBQ,\]                      (Given)    PB = AS AP = BQ \[\therefore \]\[\Delta APS\]and \[\Delta PBQ\]are congruent, \[\therefore \]      SP = PQ \[\angle SPA=\angle BQP\] and       \[\angle ASP=\angle BPQ\] \[\therefore \]      \[\angle SPQ=90{}^\circ \]