Question 270808
<pre><b>
Find m&#8736;PSQ if m&#8736;PSQ = 2y-10 and m&#8736;PRQ = y+35

[A] 60         [B] 40         [C] 45           [D] 80  
{{{drawing(300,300,-2,2,-2,2,

circle(0,0,1), line(-cos(40*pi/180),sin(40*pi/180),-cos(60*pi/180),-sin(60*pi/180)), locate(-.8,.9,P), locate(.4,1.1,Q),locate(.8,-.6,R),
locate(-.6,-.9,S),
line(cos(70*pi/180),sin(70*pi/180),-cos(60*pi/180),-sin(60*pi/180)),

line(cos(40*pi/180),-sin(40*pi/180),cos(70*pi/180), sin(70*pi/180)),
line(cos(40*pi/180),-sin(40*pi/180),-cos(40*pi/180),sin(40*pi/180))



 )}}}

They are both inscribed angles which intercept to same arc PQ, so their
measures are equal, so we have the equation:

{{{2y-10=y+35}}}
{{{y="45°"}}}

Substituting 45° in either {{{2y-10}}} or {{{y+35}}} gives

{{{2("45°")-"10°"="90°"-"10°"="80°")}}}

The correct choice is 80, choice [D]

Edwin</pre>