Anger and critical thinking - how can those possibly coexist? You cannot have good critical thinking and problem-solving skills when you are angry. And this is the very reason you must work with your teen to help him or her with learning to manage his anger.
Being emotionally overwhelmed whether one is anger or anxious stops the ability to think through a problem and find a solution. So how do you help your teen with this? The first thing to do is to model for your teen how you handle being angry. If your teen sees you handle anger in a positive way, he will often model this behavior. Unfortunately, he will model negative ways to handle anger if that is what you teach him by your behavior.
Discuss with your teen the concept of taking a "personal time out." This means learning how to take ten minutes or longer if needed to separate oneself from the issue or person which is contributing to the feelings of anger. Having a discussion about your teen going to a separate room for a personal time out can be very beneficial. Then discuss with your teen how to think through the issues ONCE HE IS CALM. Learning to not make decisions when angry is a big step in critical thinking.
So teaching your teen an immediate way to lower anger and then teaching him how to think through his problem and give this time before making a decision helps build his critical thinking skills.