Which of the following defines the interior angle theorem ?

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The formula for calculating the sum of the interior angles of a polygon is the following:S = (n - 2)*180.

n represents the number of sides and S represents the sum of all of the interior angles of the polygon.

The angles that lie inside a shape, are said to be interior angles, or the angles that lie in the area bounded between two parallel lines that are intersected by a transversal are also called interior angles.

All the above

answer is D.

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Detailed Solution

The interior angle theorem states that “the sum of the measures of the interior angles of a polygon with n number of sides is

. Let's check whether the statement is true for the triangle or not.
We know that a triangle has three sides (n=3) and the sum of the interior angles is A triangle is always a convex polygon. We apply the theorem and obtain the sum of the angles

.
We know that for both quadrilaterals the sum of the angles is 360∘. We apply the theorem for a quadrilateral with the number of sides n=4 and we have (n−2)

= (4−2)

So the quadrilateral satisfies the theorem. Similarly, we can check pentagon (n=5), hexagon (n=6) and so on.
So, Option 4 is correct.

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