εὐαγγελίῳ. [8 verses](noun sg neut dat) "Good news" is  euaggelion, a "reward of good tidings," a "thank offering for good tidings, " "good news," and "good tidings." Originally, this term described a reward, like a tip, given to a messenger who brought good news.The root is -aggelia, which means "message." The masculine form, -aggelos," means "messenger." This form is neuter. -- "Good news" has come to mean the Jesus story itself, i.e. the Gospel, but Jesus doesn't seem to use it that way at all. This is Jesus's only used of the noun form of the word. The phrase doesn't mean the "good news itself." Instead it means "the reward for bringing good news.

εὐαγγελίζονται: [5 verses] (3rd pl pres ind mp) "Preach" is from euaggelizo. which means "bring good news," "announce good things," "preach or proclaim as glad tidings," and, in the passive, "receive good news." -- (CW) "Preach" is translated from a Greek word that means to"bring good news," and, in the passive, "receive good news." It is either passive or in a form which indicates the subject acting on itself. It is in the form of "to bring good news. It comes before the word translated as "must."   This religious "preached" is more specific than the word's meaning. CW --Confusing Word --  This religious "preached"transition is more specific than the word's more general meaning.

εὐχαριστῶ [2 verses](1st sg pres ind act) "I thank" is from eucharisteo, which means "to bestow a favor on," "to oblige," "to be thankful," "to return thanks," and "to be received with thanks."  - The Greek word translated as "thank" means both to offer a favor and to be grateful for receiving favors. The two ideas were tied together. The idea is that bestowing a favor automatically creates thankfulness. This is related to the sense of "debt" in the Gospels, which is a topic Christ addresses more commonly, most noticeably in the Lord's Prayer.

Εὐδία, [1 verse](noun sg fem nom) "Fair weather" is eudia, which means "fair weather" or "fine weather," and is a metaphor for "tranquility" and "peace."  - "Fair weather" is translated from a Greek word that means literally, "good weather." It is a metaphor for tranquility and peace. Jesus only uses this word in one verse.

εὐδόκησεν [1 verse](verb 3rd sg aor ind act) "It is...good pleasure" is eudokeo, which means "to be well-pleased", "to be content:"., "to find pleasure in", "to consent", "to approve", "to determine", and "to resolve". Another word only used once by Jesus in the Gospels in transla - -  The Greek verb means "to be well-pleased", "to be content:", "to find pleasure in", "to consent", "to approve", "to determine", and "to resolve". The subject here is "the father" so the phrase is "he is content" or "consents". This word is used by the Father in the other Gospels to describe his attitude toward the Son.