The attached is a four-page packet that starts with the triangle sum theorem proof using 2 parallel auxiliary lines to show that the three angles of a triangle should add up to 180 degrees. The packet continues to two practice problems applying the triangle sum theorem then goes into breaking polygons down into triangles by drawing diagonals from one vertex showing that the foundation of any polygon is a triangle. The next page is a table where students fill out the number of sides in a polygon, figure out the number of triangles that it breaks into and then calculate the sum of interior angles from the number of triangles. The last row is an n-gon where students make a generalization for the sum of interior angles regarding any polygon with n sides. The next page introduces interior and exterior angles of a polygon and regular polygons with a table to summarize the formulas for interior and exterior angles of any polygon. The last page has two practice questions for polygons using a regular and non-regular polygon then providing a thought map for tackling polygon problems.
Students find this progression of content really easy to understand and with enough areas for information summary/tables that they use it as a reference sheet to look back to as they go on to other practice worksheets and problems.
I've included an editable and non-editable version as well as an answer key. Also, this is common core aligned with a non-intimidating approach!