3. A BC D

4. Let ABCD be a quadrilateral. Join AC. Clearly, ∠ 1 + ∠ 2 = ∠ A...... (i) And, ∠ 3 + ∠ 4 = ∠ C...... (ii) We know that the sum of the angles of a triangle is 180°. Angle Sum Property of a Quadrilateral Therefore, from ∆ABC, we have ∠ 2 + ∠ 4 + ∠ B = 180° (Angle sum property of triangle) From ∆ACD, we have ∠ 1 + ∠ 3 + ∠ D = 180° (Angle sum property of triangle) Adding the angles on either side, we get; ∠ 2 + ∠ 4 + ∠ B + ∠ 1 + ∠ 3 + ∠ D = 360° ⇒ ( ∠ 1 + ∠ 2) + ∠ B + ( ∠ 3 + ∠ 4) + ∠ D = 360° ⇒ ∠ A + ∠ B + ∠ C + ∠ D = 360° [using (i) and (ii)]. Hence, the sum of all the four angles of a quadrilateral is 360°. PROOF :-

8. A D B C