credible
Believable and likely to be true or trustworthy.
Credible means believable or worthy of trust. When something is credible, you have good reason to think it's true or reliable. A credible witness in court is someone whose testimony makes sense and matches the facts. A credible news source checks its information carefully before publishing. When your friend has a credible excuse for missing your birthday party (maybe they were sick with the flu), you believe them because the explanation rings true.
The opposite of credible is incredible, which can mean either “unbelievable” or, confusingly, “amazingly good.” But when something lacks credibility, we usually say it's not credible or lacks credibility to avoid confusion.
Scientists build credibility by showing their work and letting others verify their results. Teachers build credibility by demonstrating they know their subject and treat students fairly. You build credibility by being honest, keeping your promises, and admitting when you don't know something instead of making things up.
Notice that credibility takes time to build but can be lost quickly. If someone tells you three true things and one obvious lie, you start doubting everything they say. Being credible matters because once people stop believing you, even your true statements might not be taken seriously.