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

From triangle ABD we have:a + b_{1} + d_{1} = 180º. (1)

From triangle BCD we have:

c + b_{2} + d_{2} = 180º. (2)

Adding (1) with (2) we get:

a + b_{1} + d_{1} + c + b_{2} + d_{2} = 180º + 180º

a + b_{1} + d_{1} + c + b_{2} + d_{2} = 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:

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

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