The measure of the sum of the interior angles of a convex polygon with n sides is given by [tex]S=(n-2)180[/tex]
A polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and finite number of sides.
A quadrilateral can be defined as a type of polygon that is made up of four (4) sides, four (4) vertices, four (4) edges and four (4) angles.
Mathematically, the measure of the sum of the interior angles of a convex polygon with n sides is given by:
[tex]S=(n-2)180[/tex]
In Geometry, the measure of the sum of the angles of a convex quadrilateral, pentagon, and a nonagon is equal to 360 degrees.
For a regular polygon:
Mathematically, the measure of an interior angle with n sides is given by;
[tex]A=(2n-4)90[/tex]
For a regular octagon:
Mathematically, the measure of an interior angle is equal to 135 degrees.
Lastly, the sum of the measure of the exterior angles, one at each vertex of a convex polygon is equal to 360 degrees.
Read more on quadrilateral here: https://brainly.com/question/16691874