Best Answer

Proof:Draw any quadrilateral. Draw a line from one corner to the opposite corner. This line is called a diagonal and quadrilaterals have two of them. Some quadrilaterals won't have both diagonals completely within the quadrilateral but they all have at least one diagonal with this property. Using this diagonal it is clear to see the quadrilateral is divided into 2 triangles and that adding up all the angles in the triangle will give you the sum of the quadrilateral. Since the angle sum of any triangle is 180 degrees and we have two triangles we have 360 degrees.

Generalisation:Any polygon with n corners (called vertices) has n edges. You can take a polygon with n-1 vertices for n>=4 and stick a triangle onto one edge and you increase the angle sum by 180 degrees. So the angle sum of a polygon with n vertices is 180*(n-2) for n>=3.

Generalisation:Any polygon with n corners (called vertices) has n edges. You can take a polygon with n-1 vertices for n>=4 and stick a triangle onto one edge and you increase the angle sum by 180 degrees. So the angle sum of a polygon with n vertices is 180*(n-2) for n>=3.

Q: Why does all quadrilaterals add up to 360 degrees?

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

All quadrilaterals have a total of 360 degrees

All quadrilaterals are 4 sided shapes that have 4 interior angles that add up to 360 degrees.

Not exactly but all quadrilaterals have 4 sides and 4 interior angles that add up to 360 degrees.

The all have 4 sides and their 4 interior angles add up to 360 degrees

They all have 4 sides and interior angles add up to 360 degrees.

Related questions

All 4 sided quadrilaterals have 4 interior angles that add up to 360 degrees

All quadrilaterals have 4 interior angles that add up to 360 degrees.

360 degrees

All quadrilaterals have a total of 360 degrees

Yes the 4 interior angles of all quadrilaterals add up to 360 degrees

The interior angles of all quadrilaterals add up to 360 degrees.

All quadrilaterals are 4 sided shapes that have 4 interior angles that add up to 360 degrees.

All quadrilaterals are 4 sided polygons having 4 interior angles that add up to 360 degrees

Not exactly but all quadrilaterals have 4 sides and 4 interior angles that add up to 360 degrees.

A trapezium is a quadrilateral and, as with all quadrilaterals, its interior angles sum to 360 degrees.

Not always but all 4 sided quadrilaterals have 4 interior angles that add up to 360 degrees

All polygons with four angles (quadrilaterals) have a inner angle sum of 360 degrees.