Question

give me some angle sum properties of polygon

Answer 1

for triangle =sum of all sides is 180 degree
for quadrilateral =sum of all sides is 360 degre

Answer 2

 properties of polygons

In your exam, you might be asked to find angles of polygons.

The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180° where n is the number of sides of the polygon.

This formula comes from dividing the polygon up into triangles using full diagonals.

We already know that the interior angles of a triangle add up to 180°. For any polygon, count up how many triangles it can be split into. Then multiply the number of triangles by 180.



This quadrilateral has been divided into two triangles, so the interior angles add up to 2 × 180 = 360°.



This pentagon has been divided into three triangles, so the interior angles add up to 3 × 180 = 540°.

In the same way, a hexagon can be divided into 4 triangles, a 7-sided polygon into 5 triangles etc.

Can you see the pattern forming? The number of triangles is equal to the number of sides minus 2.