Explain how the formula for finding the sum of the interior angle measures of a polygon is derived.

Explanation:

Here's one way:

Choose a point P interior to the polygon and draw a segment from that point to each vertex. These segments will divide an n-sided polygon into n triangles. These will have a total angle measure of ...

  total interior angles of n triangles = 180°×n

The n angles having a vertex at point P have a sum of 360°. Subtracting this total from the total of all triangles gives the sum of interior angles around the perimeter of the polygon: 180°×n - 360° = 180°×(n -2).

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step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.