#### notes

The sum of the angles of a quadrilateral is 360º. This can be verified by drawing a diagonal and dividing the quadrilateral into two triangles. Let ABCD be a quadrilateral and AC be a diagonal in following fig.

You know that

∠ DAC + ∠ ACD + ∠ D = 180° (1)

Similarly, in ∆ ABC,

∠ CAB + ∠ ACB + ∠ B = 180° (2)

Adding (1) and (2), we get

∠ DAC + ∠ ACD + ∠ D + ∠ CAB + ∠ ACB + ∠ B = 180° + 180° = 360°

Also, ∠ DAC + ∠ CAB = ∠ A and ∠ ACD + ∠ ACB = ∠ C

So, ∠ A + ∠ D + ∠ B + ∠ C = 360°.

i.e., the sum of the angles of a quadrilateral is 360°.