How do I prove that angles of a quadrilateral equal 360?

Md Ariful Islam

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Dr. Md Rushad Rahman

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Draw your diagonals. Four triangles appear, forming 12 angles. We know that the sum of these angles is going to be 180 x 4, so 720°. The angles that join in the middle of the polygon form a whole angle, 360°. So the sum of the other angles, which equal the sum of the angles of the quadrilaterals is 720-360°. This demonstration shows that if you add a side to the polygon, you add a triangle, so 180° to the total, and the center stays 360°. Which gives you the formula for the sum of the angles based on the number of sides N: 180 x N - 360. which you can factor as 180 (N-2).

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