What is the sum of this polygon's interior angles?

init({
range: [ [ -5, 5 ], [ -1, 5 ] ],
scale: [ 40, 40 ]
});
graph.polygon = new Polygon( SIDES );
graph.polygon.draw();
CLONE = graph.polygon.clone();

There are a couple ways to approach this problem.

Does it help to remember that there are 180 degrees in a triangle?

Since this polygon has `SIDES` sides, we can draw `SIDES` triangles that all meet in the center.

graph.polygon.drawRadialDiagonals();

We can combine all the triangles' angles, and then we must subtract 360 degrees because the circle in the middle is extra.

`\begin{align*}&`

`SIDES` \times 180^{\circ} - 360^{\circ} \\
&= `SIDES * 180`^{\circ} - 360^{\circ} \\
&= `ANSWER`^{\circ}\end{align*}

An alternative approach is shown below.

We can use four of the `cardinal( SIDES )` sides to make 2 triangles, as shown in orange.

init({
range: [ [ -5, 5 ], [ -1, 5 ] ]
});
graph.polygon = CLONE;
graph.polygon.draw();
graph.polygon.drawDiagonals( randRange( 0, SIDES - 1 ) );

There `plural( "is", SIDES - 4 )` `plural( SIDES - 4, "side" )` between the orange triangles, to make `SIDES - 4` additional `plural( "triangle", SIDES - 4 )`.

We chopped this polygon into `SIDES - 2` triangles, and each triangle's angles sum to 180 degrees.

`SIDES - 2` \times 180^{\circ} = `ANSWER`^{\circ}

Again, we have found that the sum of the polygon's interior angles is `ANSWER` degrees.

What is the sum of this polygon's exterior angles?

init({
range: [ [ -6, 6 ], [ -2, 7 ] ]
});
graph.polygon = new Polygon( SIDES );
graph.polygon.draw();

The exterior angles are shown above.

graph.polygon.drawExteriorAngles();

graph.polygon.animateExteriorAngles( randRange( 0, SIDES - 1 ) );

The exterior angles fit together to form a circle, summing to 360 degrees.