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Sum of measurements of internal angles of a convex quadrilateral


The sum of the internal angles of a convex quadrilateral is 360º.

We can prove this statement by decomposing the quadrangle ABCD into triangles ABD and BCD.

From triangle ABD we have:

a + b1 + d1 = 180º. (1)

From triangle BCD we have:

c + b2 + d2 = 180º. (2)

Adding (1) with (2) we get:

a + b1 + d1 + c + b2 + d2 = 180º + 180º
a + b1 + d1 + c + b2 + d2 = 360º

a + b + c + d = 360º

Comments:

1. We have a general formula for determining the sum of the internal angles of any convex polygon:

si = (n - 2) · 180º, where no is the number of sides of the polygon.

2. The sum of the external angles of any convex polygon is 360 °.

sand = 360º

Next: Notable Quads - Parallelogram