Hung vs. Hanged

Hi,
I made test in English and faced the challenge. Can you explain something to me?

The sentence was:
Since the abolition of capital punishment in this country murderers are not hung if they are found guilty.

I should find any mistake in this sentence and I found it. The mistake was hung.

I correct the sentense and it became like that:
Since the abolition of capital punishment in this country murderers are not hang if they are found guilty.

But! the answer was like that:
Since the abolition of capital punishment in this country murderers are not hanged if they are found guilty.

I understand that my answer was incorrect but the verb to hang is an irregular verb, isn’t it? And it hasn’t such form as hanged.

.
Although many people now use ‘hung’ for capital punishment, some grammarians still like the distinction between the two verbs:

hang / hung / hung (for clothes in your closet, etc)
hang / hanged /hanged (for capital punishment, suicide, etc)
.

And it’s always been “hung” for “hung, drawn and quartered”, hasn’t it?

Slightly off-topic, I found this and interesting use of “hung”:

Thanks, I didn’t know the difference. =)