Question

geometry 6 - 1: the polygon angle - sum theorems
how does the number of sides of a convex polygon, n, relate to the sum of measures of its interior angles?
you know that the sum of the interior angle measures of a triangle is 180°. decompose polygons into triangles and look for a pattern.
to decompose a convex polygon into triangles, construct all diagonals from one vertex.
for n = 4 (2 triangles), n = 5 (3 triangles), n = 6 (4 triangles), n = 7 (5 triangles), n sides (n - 2 triangles)
there are n - 2 triangles in every n - sided polygon. each triangle has an angle sum of 180. interior angle sum of an n - sided polygon = 180·(n - 2)
questions 1 & 2

1. interior means (with a select dropdown)
2. exterior means (with a select dropdown)

Explanation:

1. Interior means

In the context of polygon angles, "interior" refers to the angles that are inside the polygon, formed by its sides. For a convex polygon, these are the angles between two adjacent sides, lying within the closed shape of the polygon.

For polygon angles, "exterior" angles are formed by one side of the polygon and the extension of an adjacent side, lying outside the closed shape of the polygon. Each exterior angle is supplementary to its corresponding interior angle (for convex polygons).

Answer:

(Assuming typical options, e.g., if options were "Inside the polygon", "Outside the polygon", "On the vertex", the correct one would be) Inside the polygon (exact wording depends on dropdown options, but the concept is angles within the polygon's boundary).

2. Exterior means