General enunciation: We have to prove that the sum of the angles of a quadrilateral is equal to 4 right angles.
Particular enunciation: Let four angles of a quadrilateral ABCD be ∠A, ∠B, ∠C, and ∠D. We have to prove that sum of the four angles equal to 4 right angles that is ∠A+∠B+∠C+∠D= 4 right angles.
Construction: We join A with C and B with D.
Proof: We know the sum of the three angles of a triangles is equal to two right angles.
From triangle ABC
Again from triangle ADC
Now adding (1) and (2) we have,
⇒(∠BAC+∠DAC)+ ∠ABC+(∠BCA+∠DCA)+ ∠ADC=3600
⇒ ∠BAD+∠A BC+∠BCD+∠ADC=3600
⇒∠A+∠B+∠C+∠D=3600=4 right angles. (Proved)