Reflecting $R$ from line $SP$, thus we know that $SR'=PQ$ and $P,Q,S,R'$ are on the same circle, thus $PQSR'$ is an isosceles trapezoid, which means that $PQS=QSR'=85^{\circ}$, which means that $\angle RSP=\frac{\angle RSR'}{2}=\frac{25^{\circ}+85^{\circ}}{2}=55^{\circ}$, thus $\angle SPQ= 360^{\circ}-\angle PQR-\angle QRS - \angle RSP=360^{\circ}-110^{\circ}-130^{\circ} - 55^{\circ}=65^{\circ}.$ [asy][asy] /* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */ import graph; size(8cm); real labelscalefactor = 0.3; /* changes label-to-point distance */ pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ pen dotstyle = black; /* point style */ real xmin = -2.6351986743130573, xmax = 6.973807231882933, ymin = -12.201178338237488, ymax = 6.680854246665095; /* image dimensions */ /* draw figures */ draw((1.9341188195423784,0.4148416539883482)--(0.4558102185891493,2.3971190961756297), linewidth(1)); draw((0.4558102185891493,2.3971190961756297)--(1.8129303837853108,4.4642535946238535), linewidth(1)); draw((1.8129303837853108,4.4642535946238535)--(4.268787306544951,4.753367676588741), linewidth(1)); draw((4.268787306544951,4.753367676588741)--(1.9341188195423784,0.4148416539883482), linewidth(1)); draw((0.4558102185891493,2.3971190961756297)--(4.268787306544951,4.753367676588741), linewidth(1)); draw((1.8129303837853108,4.4642535946238535)--(1.9341188195423784,0.4148416539883482), linewidth(1)); draw(circle((2.9116671413487882,2.6862331781405175), 2.47281624417522), linewidth(1)); draw((1.9341188195423784,0.4148416539883482)--(5.380418212642235,2.54449988831662), linewidth(1)); draw((5.380418212642235,2.54449988831662)--(4.268787306544951,4.753367676588741), linewidth(1)); /* dots and labels */ dot((1.9341188195423784,0.4148416539883482),dotstyle); label("$P$", (2.001314665040253,0.5828312677330332), NE * labelscalefactor); dot((0.4558102185891493,2.3971190961756297),dotstyle); label("$Q$", (0.5230060640870234,2.565108709920315), NE * labelscalefactor); dot((1.8129303837853108,4.4642535946238535),dotstyle); label("$R$", (1.8837219354189731,4.631380958979939), NE * labelscalefactor); dot((4.268787306544951,4.753367676588741),dotstyle); label("$S$", (4.336370296091377,4.916963302345903), NE * labelscalefactor); dot((5.380418212642235,2.54449988831662),dotstyle); label("$R'$", (5.445101746806299,2.716299362290531), NE * labelscalefactor); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); /* end of picture */ [/asy][/asy]