News organizations are increasingly using social media to reach out to their audience aimed at raising their attention and engagement with news. Given the continuous decrease in subscription rates and audience trust in news media, it is imperative for news organizations to understand factors contributing to their relationships with the audience. Using Twitter data of 315 U.S. newspaper organizations and their audiences, this study uses multiple regression analysis to examine the influence of key news organization characteristics on audience engagement with news: (1) trustworthiness computed by the Trust Scores in Social Media (TSM) algorithm; (2) quantity of tweets; and (3) skillfulness of Twitter use. The results show significant influence of a news organizations' trustworthiness and level of Twitter activity on its audiences' news engagement. Methods to measure trustworthiness of news organizations and audience news engagement, as well as scalable algorithms to compute them from large-scale datasets, are also proposed.