Question

select the correct answer from each drop - down menu.
determine the number of triangles formed from triangulated polygon abcdefg. determine the total interior angle measure in each triangle and the total interior angle measure of the polygon.
polygon abcdefg may be divided into triangles.
the total interior angle measure of each triangle is
the total interior angle measure of polygon abcdefg is

Explanation:

Step1: Find the number of triangles

For an \(n -\)sided polygon, the number of triangles formed by triangulation (drawing non - overlapping diagonals from one vertex) is \(n - 2\). The polygon \(ABCDEFG\) has \(n=7\) sides. So the number of triangles is \(n - 2=7 - 2 = 5\).

Step2: Find the sum of interior angles of a triangle

By the triangle angle - sum theorem, the sum of the interior angles of a triangle is \(180^{\circ}\).

Step3: Find the sum of interior angles of the polygon

Since the polygon is divided into \(k = 5\) triangles and the sum of interior angles of each triangle is \(S_{\triangle}=180^{\circ}\), the sum of interior angles of the polygon \(S=(n - 2)\times180^{\circ}\). Substituting \(n = 7\), we get \(S=(7 - 2)\times180^{\circ}=900^{\circ}\).

Answer:

Polygon \(ABCDEFG\) may be divided into \(5\) triangles. The total interior angle measure of each triangle is \(180^{\circ}\). The total interior angle measure of polygon \(ABCDEFG\) is \(900^{\circ}\).