Question

prove that the sum of the four. angles of a qadirilatral is 360

Answer 1

BD is a diagonal of quadrilateral ABCD.
InABD,
angle ABD+angle BAD+angle ADB=180
InBCD,
angle BCD+angle CBD+angle BDC=180

By adding both, we get,
angle ABD+angle BAD+angle ADB+angle BCD +angle CBD+angle BDC=180+180
angle BAD+angle BCD+angle ABD+angle CBD +angleADB+angle CDB=360
angle BAD+angle BCD+angle ABC+angle ADC =360

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