opportune
Happening at just the right and most helpful time.
Opportune means happening at exactly the right time, when conditions are perfect for success. When rain falls at an opportune moment during a drought, it saves the crops. When a friend offers help just as you're struggling with homework, that's opportune timing.
The word describes moments when circumstances align in your favor. If you're looking for a summer job and your neighbor mentions they need help the very next day, that's an opportune opportunity. If you arrive at the library just as someone returns the book you desperately need, that's opportune.
Opportune is different from simply lucky. It suggests that the timing makes something especially useful or valuable. A joke told at an opportune moment might break tension in an argument. A question asked at an opportune time might help a confused classmate finally understand a lesson.
The opposite would be inopportune, meaning badly timed: like when your pencil breaks in the middle of a timed test, or when your little brother interrupts right as you're explaining something important.