## Solution:

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

∠BAC+∠ABC+∠BCA=180^{0}—————————————–(1)

Again from triangle ADC

∠DAC+∠ADC+∠DCA=180^{0}——————————————(2)

Now adding (1) and (2) we have,

∠BAC+∠ABC+∠BCA+∠DAC+∠ADC+∠DCA=360^{0}

⇒(∠BAC+∠DAC)+ ∠ABC+(∠BCA+∠DCA)+ ∠ADC=360^{0}

⇒ ∠BAD+∠A BC+∠BCD+∠ADC=360^{0}

⇒∠A+∠B+∠C+∠D=360^{0}=4 right angles. **(Proved)**