Question

6
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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: Recall polygon - triangle relation

The number of triangles formed by triangulating an $n$-sided polygon is $n - 2$. The polygon $ABCDEFG$ has $n=7$ sides. So the number of triangles is $7 - 2=5$.

Step2: Recall interior - angle of a triangle

The sum of the interior - angles of any triangle is $180^{\circ}$.

Step3: Calculate the sum of interior - angles of the polygon

The sum of the interior - angles of a polygon is equal to the number of triangles formed by triangulating the polygon times the sum of the interior - angles of a triangle. Since the number of triangles is 5 and the sum of interior - angles of a triangle is $180^{\circ}$, the sum of the interior - angles of the heptagon $ABCDEFG$ is $5\times180^{\circ}=900^{\circ}$.

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 $900^{\circ}$.