Question

Can you tell what is the sum of all interior angles of a quadrilateral , pentagon , hexagon and so on

Answer 1

From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times 180 degrees to find the sum of all the interior angles of a pentagon, which is 540 degrees.

We can use the same way for all polygons

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Answer 2

Answer:

We know,

The sum of interior angles of a polygon =n-2x180°

So,

I) sum of interior angles of a quadrilateral

=n-2x180°

=4-2x180° (as quadrilaterals have four sides)

=2x180°

=360°

ii) sum of interior angles of pentagon

=n-2x180°

=5-2x180° (as pentagons have five sides)

=3x180°

=540°

iii) sum of interior angles of hexagon

=n-2x180°

=6-2x180° ( as hexagons have six sides)

=4x180°

=720°

Similarly, we can find sum of interior angles of polygons of any side.