theorem 1 (Exterior angle sum property) if the sides of quadrilateral are produced in order the sum of four exterior angles so formed is `360^@`.

Explanation

Given: ABCD is a quadrilateral.
To proof: `/_1+/_2+/_3+/_4=360^@`
Now, by angle sum property of quadrilateral:
`/_A+/_B+/_C+/_D=360^@`.......(i)
From figure, by sum of linear angles is `180^@`
`/_A+/_1=180^@`.......(ii)
`/_B+/_2=180^@`.......(iii)
`/_C+/_3=180^@`.......(iv)
`/_D+/_4=180^@`.......(v)
Adding equations (ii), (iii), (iv) and (v), we get
`/_A+/_B+/_C+/_D+/_1+/_2+/_3+/_4=180^@\+180^@\+180^@\+180^@`
By using equation (i), we get
`360^@\+/_1+/_2+/_3+/_4=720^@`
`/_1+/_2+/_3+/_4=720^@-360^@`
`/_1+/_2+/_3+/_4=360^@`.
Hence proved that if the sides of quadrilateral are produced in order the sum of four exterior angles so formed is `360^@`.