Question 898741
Each interior angle of a regular polygon is thrice each exterior angle.
Find the number of side of the polygon.
<pre>
An interior angle and an exterior angle at a vertex of a polygon
are supplementary.

Let the exterior angle be X.
Then the interior angle is 3X.
Since they are supplementary,

X + 3X = 180°
    4X = 180°
     X = 45°

So each exterior angle is 45°, and each interior angle is 3×45°=135°.

Let the number of sides be N.

The sum of the exterior angles of a polygon is 360°

Since the polygon is regular, each interior angle is {{{"360°"/N}}}
So

{{{"360°"/N}}}{{{""=""}}}{{{"45°"}}}

Multiply both sides by N

{{{"360°"}}}{{{""=""}}}{{{"45°"N}}}

Divide both sides by 45°

{{{8}}}{{{""=""}}}{{{N}}}

It's an 8-sided regular polygon, a regular octagon.
In the regular octagon below, the 135° angle is an INTERIOR angle,
and the 45° angle is an exterior angle.  

{{{drawing(400,400,-1.2,1.2,-1.2,1.2,
green(line(0,1,4,-.6568542495)),

red(arc(0.70710678,0.70710678,.6,-.6,158,293)),
red(arc(0.70710678,0.70710678,.68,-.69,293,338)),

locate(.5,.66,"135°"),locate(.8,.6,"45°"),
line(1,0,0.70710678,0.70710678),
line(0.70710678,0.70710678,0,1),
line(0,1,-0.70710678,0.70710678),
line(-0.70710678,0.70710678,-1,0),
line(-1,0,-0.70710678,-0.70710678),
line(-0.70710678,-0.70710678,0,-1),
line(0,-1,0.70710678,-0.70710678),
line(0.70710678,-0.70710678,1,0)  )}}}

Edwin</pre>