Question

in given figure ABCD IS A SQUARE IF ANGLE PQR=90DEGREES AND PB= QC .PROVE THAT ANGLE QPR=45DEGREE

Answer 1

Since PBCR becomes rectangle  

∴ PB=RC=x  

⇒AP=x

If QC=RC=x ∴∠CRQ=∠RCQ= 45^{0}  

Since ∠PRC= 90^{0}  

∴∠PRQ= 45^{0}  

and sum of angles a triangle is  180^{0}  

∴∠PQR= 90^{0}   and ∠PRQ= 45^{0}  

∴∠QPR= 180^{0} -( 90^{0} + 45^{0} )= 45^{0}