The principle
An anxious child needs a non-anxious parent. That is harder than it sounds, and it is the whole task. When you panic, you teach your teenager that the situation deserves panic.
What helps
Slow your breathing before the conversation. Sit down rather than stand over them. Ask one question and listen to the whole answer. Resist the urge to solve. Most anxious teenagers do not want the problem fixed in the first five minutes. They want to know it can be heard without breaking you.
What does not help
Reassurance like "there is nothing to worry about" is felt as dismissal. Comparisons to your own teenage years are felt as competition. A long lecture on perspective is felt as a closing argument. Save them all.
When to seek help
When anxiety is interrupting sleep, school attendance, or relationships for more than a few weeks, the family is not failing. It is time for a third party. That is not surrender. It is good parenting.