Complex sentence: In 1980, after being turned down in favor of Dan Rather to succeed Cronkite as weeknight anchor of the CBS Evening News, Mudd chose to leave CBS News and accepted an offer to join NBC News.
Split into simpler sentences: In 1980, Mudd and Dan Rather were in contention to succeed Walter Cronkite as weeknight anchor of the CBS Evening News. Mudd then chose to leave CBS News and accepted an offer to join NBC News.