Question 174527
<pre><font size = 4 color = "indigo"><b>
We start with a circle, then we draw in the
150° America "piece of pie"
{{{drawing(300,300,-1.3,1.3,-1.3,1.3, 

circle(0,0,1))}}}{{{drawing(300,300,-1.3,1.3,-1.3,1.3, 

circle(0,0,1), line(0,0,1/2,sqrt(3)/2),
line(0,0,0,-1),
locate(.4,0,America),locate(0,.03,"150°") 
  )}}}

Now we calculate the number who would like
to visit America with ratio-and-proportion

Let N represent the number who would like to visit
America:

Then N is to the total 3240 people as the 150°-angle
is to the total 360 degrees in the whole circle.

{{{matrix(4,3, N/3240, "=", "150°"/"360°",
              "cross multiply","","",
              "360°"N, "=", "486000°",
              N, "=", 1350 )}}}

Then we draw in the 90° Africa "piece of pie"

{{{drawing(300,300,-1.3,1.3,-1.3,1.3, 

circle(0,0,1), line(0,0,1/2,sqrt(3)/2),locate(.45,-.15,"(1350)"),
line(0,0,0,-1), line(-1,0,0,0), locate(0,.03,"150°") 
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.2,-.1,"90°")
  )}}}

Now we calculate the number who would like
to visit Africa with ratio-and-proportion

Let N represent the number who would like to visit
Africa:

Then N is to the total 3240 people as the 90°-angle
is to the total 360 degrees in the whole circle.

{{{matrix(4,3, N/3240, "=", "90°"/"360°",
              "cross multiply","","",
              "360°"N, "=", "291600°",
              N, "=", 810 )}}}


Now we have accounted for 150°+90° or 240° of the 360° in the
whole circle.  Therefore if we subtract 240° from 360°, we get
120° for both the Asia and Australia pieces of pie together. 
So we will let x° be the number of degrees for the Asia piece
of pie, and then subtract x° from 120° to get 120°-x° for the 
Australia piece of pie.

{{{drawing(300,300,-1.3,1.3,-1.3,1.3, 
circle(0,0,1), line(0,0,1/2,sqrt(3)/2),locate(.45,-.15,"(1350)"),
line(0,0,0,-1), line(-1,0,0,0), line(0,0,-.3090169944,.9510565163),
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.7,.5,Asia),
locate(0,.03,"150°"), locate(-.2,-.1,"90°"),locate(-.7,-.45,"(810)"),
 locate(-.2,.2,"x°"), locate(-.2,-.1,"90°")
  )}}}{{{drawing(300,300,-1.3,1.3,-1.3,1.3,circle(0,0,1), line(0,0,1/2,sqrt(3)/2),
line(0,0,0,-1), line(-1,0,0,0), line(0,0,-.3090169944,.9510565163),locate(.45,-.15,"(1350)"),
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.7,.5,Asia),
locate(-.2,.9,Australia),locate(0,.03,"150°"), locate(-.2,-.1,"90°"),
locate(-.15,.6,"120°-x°"), locate(-.2,.2,"x°"), locate(-.7,-.45,"(810)")
  )}}}

We could go straight for the answer here, but so we 
can draw the pie graph accurately we calculate the angle
of the Asia piece of pie with ratio-and-proportion:

The angle of the Asia piece of pie is to the angle of 
the Australia piece of pie as 3 is to 2  

{{{matrix(6,3, "x°"/"120°-x°", "=", 3/2,
              "cross multiply","","",
              2x, "=", "3(120°-x°)",
              2x, "=", 360-3x, 
              5x, "=", "360°",
               x, "=", "72°")  
}}}          

Therefore the angle of the Australia piece of
pie is 120°-72° or 48°

{{{drawing(300,300,-1.3,1.3,-1.3,1.3, 
circle(0,0,1), line(0,0,1/2,sqrt(3)/2),locate(.45,-.15,"(1350)"),
line(0,0,0,-1), line(-1,0,0,0), line(0,0,-.3090169944,.9510565163),
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.7,.5,Asia),
locate(0,.03,"150°"), locate(-.2,-.1,"90°"),locate(-.7,-.45,"(810)"),
 locate(-.25,.15,"72°"), locate(-.2,-.1,"90°"),locate(-.2,.9,Australia)
  )}}}{{{drawing(300,300,-1.3,1.3,-1.3,1.3,circle(0,0,1), line(0,0,1/2,sqrt(3)/2),
line(0,0,0,-1), line(-1,0,0,0), line(0,0,-.3090169944,.9510565163),locate(.45,-.15,"(1350)"), locate(-.2,.9,Australia),
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.7,.5,Asia),
locate(-.2,.9,Australia),locate(0,.03,"150°"), locate(-.2,-.1,"90°"),
 locate(-.25,.15,"72°"),  locate(-.7,-.45,"(810)"),
locate(-.05,.3,"48°")
  )}}}

Let N represent the number who would like to visit
Asia:

Then N is to the total 3240 people as the 72°-angle
is to the total 360 degrees in the whole circle.

{{{matrix(4,3, N/3240, "=", "72°"/"360°",
              "cross multiply","","",
              "360°"N, "=", "233280°",
              N, "=", 648 )}}}

Let N represent the number who would like to visit
Australia:

Then N is to the total 3240 people as the 48°-angle
is to the total 360 degrees in the whole circle.

{{{matrix(4,3, N/3240, "=", "48°"/"360°",
              "cross multiply","","",
              "360°"N, "=", "155520°",
              N, "=", 432 )}}}

So that's the answer and the final pie graph looks like this
{{{drawing(300,300,-1.3,1.3,-1.3,1.3,circle(0,0,1), line(0,0,1/2,sqrt(3)/2),
line(0,0,0,-1), line(-1,0,0,0), line(0,0,-.3090169944,.9510565163),locate(.45,-.15,"(1350)"), locate(-.2,.9,Australia),locate(-.7,.5-.15,"(648)"),
locate(.4,0,America),locate(-.7,-.3,Africa), locate(-.7,.5,Asia),
locate(-.2,.9,Australia),locate(0,.03,"150°"), locate(-.2,-.1,"90°"),
 locate(-.25,.15,"72°"),  locate(-.7,-.45,"(810)"),locate(0,.9-.15,"(432)"),
locate(-.05,.3,"48°")
  )}}}

Edwin</pre>