Question: How do we know that he put her in the casket?
Answer: It's obvious it was him. Nick lured Libby to that specific mausoleum, knocked her out, and dragged her into the crypt before closing the doors behind him. He then paid off the kid who acted as a decoy. Nick was motivated to get rid of her (though it was implausible that he would have left her alive before putting her into the casket). There was no-one else who could or would have done that.
Question: Why did the ex husband kill his former mistress turned wife?
Answer: Nick used Angie to help fake his death, frame Libby, and collect the insurance money which would have gone to their son, Matty. It's unclear if Nick married Angie, who became Matty's legal guardian, but he needed her to gain access to the money. He certainly didn't love her, and once he fully controlled the money, he eliminated her, as she was a liability who could have exposed him. I agree with the other answer that it also simplifies the plot by killing off a secondary character. It also shows how devious, ruthless, and sociopathic Nick is.
Answer: I don't think they explained it, but most likely for her insurance money which is the same reason Nick faked his death in the first place. But it's also possible her death was faked as well. Looking at it from the prospective of the writer, it seemed it was easier to kill her off or get rid of her somehow instead of her showing up at the end with Nick and there wouldn't be a way for Libby to kill her without facing jail time for it and it wouldn't make sense for Libby to just forgive her and let her go.
Angie's death wasn't faked. It was established and verified by the next-door-neighbor lady that she was killed in the house explosion while Nick and Maddy were conveniently away. Libby also researched old newspaper articles about the accident and the ensuing investigation. The articles also showed photos of the now-dead Angie.
Question: Given that the crime is murder why is she paroled after only six years?
Answer: To start, this film gets a lot wrong about the judicial system and law (including the whole idea that Libby can freely kill Nick because she's already been convicted of his murder). In the film, they just say she's charged with murder, but never what degree. In Washington State, 2nd degree murder generally carries a sentence of 10-18 years (not including felony-murder). However, Washington State did not offer parole at the time of the film like other states did. To be released, she'd have a hearing in front of the Washington State Clemency and Pardons Board, not a Parole Board. And it's unlikely they'd grant her a release. But in Texas for example, she could possibly get parole after serving at least half her sentence.
Answer: She apparently was convicted in a jurisdiction that used indeterminate (not determinate) sentencing, allowed a life sentence to be "with the possibility of parole" and sentencing philosophy of "let the punishment fit the criminal (not the crime). " When there is no mandatory minimum number of years to be served in prison, a convicted murderer (of various°) could actually serve relatively few years in prison with the remainder of the sentence served outside of prison (such as in a halfway house or residential treatment center, or in her own home under electronic monitoring) provided the offender does not violate the conditions of release. An offender receiving a sentence of "life imprisonment", for example, could serve the first several years in prison and then be released to a halfway house to continue "serving time" outside of prison (with supervision). The years served "in the community" are still "time served" under the sentence - only the location of serving it has changed.
Answer: Because there were exceptional and extenuating circumstances and, technically, Libby was never guilty of the crime she was convicted of and had to resort to extreme measures to prove her innocence. She may have had a gun, but it could never be proved that she held Nick at gunpoint, only that she shot him in self defense. Also, it's a movie, which often are unrealistic regarding details like that.
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