Green’s Dictionary of Slang

(Aus./N.Z.) to play the fool; note extrapolation the gay angora in cit. 1924.

1893		Kiama Indep. (NSW) 20 May. 2/3: It is to be hoped ‘Couny’ will not act the ‘giddy angora’ in England too much, or he may be sent back before the tour is over.
1900–10		Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 1: ACT THE ANGORA: slang a variant of ‘Act the goat’.
1905		Sun. Times (Perth) 26 Feb. 1/1: After declining to play because he wasn’t captain, he started to act the angora.
1914		Bulletin (Sydney) 12 Dec. 16/2: Cut out the drama, Finch, and explain why you are acting the angora?
1924		C.J. Dennis ‘’Ave a ’Eart!’ in Rose of Spadgers 15: An’, if them partin’ words weren’t meant fer me, / Well, I’m the gay angora, I suppose.
1993		E. Richards Somewhere Out There 216: Don’t act the angora with me, you old billy goat. You can point as easily as you can shrug.
2003		K. Greenwood Death before Wicket 100: Don’t act the angora, lady! No need for violence!