Why is the sum of angles in a quadrilateral equal to 360 degrees?

Answer 1

if you cut a quadrilateral on a diagonal... you form two triangles...

the sum of the angles of a triangle is 180 degrees

then the sum of two is 360 degrees...

this is thus the sum of the angles of a quadrilateral.


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Answer 2

A quadrilateral can be broken up into two triangles. And the sum of the angles of a triangle equals 180 degrees. Two triangles, so 360 degrees.

Answer 3

a quadrilateral is a polygon with four sides, the most common example is a square, which has 4 angles each equaling 90 degrees, if you add up all 4 of those you get 360 degrees. all quadrilaterals can be devided into two triangles, each of which has angles that add up to 180 degrees, so two of those make 360 degrees.

Answer 4

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Let ABCD be a quadrilateral
Join A and C
Now the quadrilateral is divided in two triangles i.e.triangles ABC and ADC
As each triangle contains 180,therefore the sum of measures of the angles of these two triangles,which is again equal to the sum of measures of the four angles of the quadrilateral,is 2 x180 or 360 degrees

Answer 5

Because if they werent the figure would not be a closed figure. For example you can have a perfect square 90 degrees on each side. But if you take and try to draw and square with 90 degree angles and one75 degree angle the figure would not be closed. there fore it would not be a quadrilateral

Answer 6

180 degrees is a flat line, and each pair of corners of a quadrilateral are supplementary angles.

Add both pairs together, and you get 360 degrees.

-Kara

Answer 7

Euclid said so (180x [sides of polygon-2]=sum of angles)

Answer 8

why is the sky blue
why does a rainbow happen
how does the positraction on a 67 chevy work

it just does

Answer 9

They're not - it's a parallelogram.