prove that the quadrileral

Prove that : the sum of the measures of all angles of a quadrilateral is 360 degree?
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ABCD is a quadrilateral. Draw a diagonal AC, dividing ABCD into two triangles: ABC and ADC. The angles of a triangle add up to 180, so BAC+ABC+BCA=180 and DAC+ADC+DCA=180. Add these two equations together:

(BAC+DAC)+ABC+ADC+(BCA+DCA)=360 which is the same as BAD+ABC+ADC+BCD=360. These are the angles of the quadrilateral.

by Top Rated User (1.2m points)

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