A cyclic quadrilateral has several properties. Among them are:
(1) Opposite angles are supplements
(2) The angle between a side and a diagonal is congruent to the angle formed by the opposite side and the other diagonal.
** In quad ABCD where the diagonals meet at T, `m/_BAC = m/_BDC` ; `/_BAC` formed by `bar(AB),bar(AC)` and `/_BDC` formed by the side opposite which is `bar(DC)` and the other diagonal `bar(DB)`
We are given that `m/_BAD+m/_BTC=180` Then
** The first two from the angle addition postulate; the second two because the exterior angle of a triangle is equal in measure to the sum of the remote interior angles.
Since the quad. is cyclic we have `m/_BAD+m/_BCD=180` or
From these we get `m/_BDC=m/_BCA`
From property (2) we have `m/_BCA=m/_BDA` .
Using substitution we get `m/_BDC=m/_BDA`
From property (2) we have `m/_BAC=m/_BDC`
And `m/_BAC=1/2m/_ADC` as required.