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How can you prove that the sum of the four interior angles in all quadrilaterals equal 360 degrees?
Wiki User
∙ 14y ago
If you accept that the sum of the angles in a triangle is 180 degrees, then picture this. A quadrilateral shape is two triangles. If you draw a line between one pair of opposite corners in quadrilateral shape, you have two triangles that share a common side. The sum of the angles in the quadrilateral must equal the sum of the angles in the two triangles. 2 x 180 = 360
Wiki User
∙ 14y ago
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What is the sum of the interior angles of a quadrilateral?
The interior angles of a quadrilateral (polygon with 4 sides and angles) sum to 360 degrees. We can find this in a couple of ways. First, noting the general formula for an n-gon: S = (n - 2)(180) where S is the sum of the interior angles in degrees and n is the number of sides of the n-gon. We find S = (4 - 2)(180) = 360 degrees. Second, the exterior angles must average 360/n degrees. In this case, 360/4 = 90 degrees. Interior angles are supplementary to exterior angles, so the average interior angle must equal 90 degrees. Finally, 4 interior angles with an average of 90 degrees means a sum of 360 degrees. Finally, consider some quadrilaterals (e.g. squares, rectangles, parallelograms, etc.). They each contain 360 degrees (e.g. four 90 degree angles).
What polygons interior angles equal 8640 degrees?
A polygon with 50 sides, given the sum of all the interior angles in 8640.
What is the sum of the interior angles of a 21 gon?
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. 3420 degrees
What is the sum of the interior angles of a regular decagon?
1440 degrees. The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees.
What is the sum of the interior angles for a 11 sided polygon?
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. 1620 degrees
Do quadrilaterals have pairs of equal angles?
Not always but all 4 sided quadrilaterals have 4 interior angles that add up to 360 degrees
How many degrees is a trapezoid equal to?
A trapezium is a quadrilateral and, as with all quadrilaterals, its interior angles sum to 360 degrees.
Why does a parallelogram equal 360 degrees?
The interior angles of all quadrilaterals sum to 360 degrees. Since a parallelogram is a quadrilateral, its interior angles must sum to 360 degrees.
Do all quadrilateral equal 360 degrees?
Yes the 4 interior angles of all quadrilaterals add up to 360 degrees
Does a quadrilateral equal 180 degress?
No because the sum of the interior angles of all quadrilaterals total 360 degrees.
What is the angle sum rule for all quadrilaterals?
The sum of all (interior) angles must equal 360 degrees
What do the interior angles of a polygon equal?
The total for the interior angles depends on the number of sides. The formula for the total of interior angles of an n-sided polygon is sum =180(n-2). This is 180 degrees for triangles, 360 degrees for quadrilaterals, and 540 degrees for pentagons.
What is the polygon whose interior angles equal 180 degrees?
It is a triangle. The formula for the total of interior angles in an n-sided polygon is 180(n-2). This is 180 degrees for triangles, 360 degrees for quadrilaterals, and 540 degrees for pentagons.
What does a square and rhombus have in common?
They are both quadrilaterals with 4 equal sides.
What type of polygon has its sum of interior angles to equal 360?
Quadrilaterals.
What Quadrilaterals equal 360 degrees?
All polygons with four angles (quadrilaterals) have a inner angle sum of 360 degrees.
Is a rhombus a square explain why?
They are both 4 equal sided quadrilaterals with opposite parallel sides but a square has 4 equal interior angles of 90 degrees whereas a rhombus has 2 equal opposite acute angles and 2 equal opposite obtuse angles.
