the supplement of an angle is one eighth of itself determine the angle and itself

Sum of an angle and its supplement is 180^o.
Let the angle be 8x^o.
So, its supplement will measure x^o

Therefore,  8x + x = 180
 ⇒  9x = 180
 ⇒  x = 20
∴  8x = 160
Thus, the required angle is 160^o and its supplement measures 20^o.