What is the sum total of the interior angles of any quadrilateral?

Solution:

A quadrilateral is a polygon with four sides and four angles.

In the above figure, ABCD is a quadrilateral with diagonal AC.

⇒ The diagonal AC divides the quadrilateral into two triangles.

Let us consider the triangle ABC and ADC are the two triangles.

By using the angle sum property of the triangle, we know that

⇒ The sum of interior angles of a triangle is 180º.

So, the sum of interior angles of triangle ABC + sum of interior angles of triangle ADC will be:

⇒ 180º + 180º

⇒ 360º

Thus, the sum total of the interior angles of any quadrilateral is 360º.

What is the sum total of the interior angles of any quadrilateral?

Summary:

The sum of the interior angles of any quadrilateral is 360°.