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Regularities in geometry

1. SUM OF INTERIOR ANGLES OF A TRIANGLE.

Notes to next figure.
To the left is a triangle with the measure of its three interior angles.
Right angles are placed one after the other. Check it
moving the vertices of the triangle.

What do you notice about the sum of the three angles?
Move the vertices and see if your conjecture is true for any triangle.

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2. SUM OF INTERIOR ANGLES OF A RING.

What about the sum of the interior angles of quadrilaterals? Research
dedúcelo the figure and the same.

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3. SUM OF INTERIOR ANGLES OF A PENTAGON.

Following the above reasoning as follows add the interior angles of a pentagon.

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4. GENERALIZED

Find a general formula that allows you to calculate the sum of the interior angles of any polygon if you know how many sides does.
For example: How much are the interior angles of a polygon with 12 sides?

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