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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.
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Earn +20 ptsQ: Why does all quadrilaterals add up to 360 degrees?
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Continue Learning about Geometry
Are All quadrilaterals are similar to each other?
Not exactly but all quadrilaterals have 4 sides and 4 interior angles that add up to 360 degrees.
What is true about all quadrilaterals?
The all have 4 sides and their 4 interior angles add up to 360 degrees
What property is common to all quadrilaterals?
They all have 4 sides and interior angles add up to 360 degrees.
What do all parallelograms have in common?
They are all 4 sided quadrilaterals and their 4 interior angles add up to 360 degrees
How many degrees are their in a arrowhead?
An arrowhead is a quadrilateral and in common with all quadrilaterals its 4 interior angles add up to 360 degrees.
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