Given that, #PR# is the diameter of circle and #/_RPS,/_QPR,/_QRP, and /_PRS# form an #AP#. Also, #/_RPS=15^@#
Let #/_QPR=x and /_PRS=y#.
In #DeltaPRS, /_PRS+/_PSR+/_PRS=180#
#rarr15^@+/_PRS+90^@=180^@#
#rarr/_PRS=75^@#
If three numbers #a,b,c# are in #AP# then #a+c=2b#
#15^@,x,y# and #x,y,75^@# are in #AP# as #15^@,x,y,75^@# are in AP .
So, #15^@+y=2x#.....[1]
and #x+75^@=2y#.....[2]
From [1], #x=(15^@+y)/2#
Putting the value of #x# in eqn [2],
#rarr(15+y^@)/2+75^@=2y#
#rarr(15^@+y+150^@)/2=2y#
#rarr165^@+y=4y#
#rarry=/_QRP=55^@#
So, the correct option is (1).
