The first step would be to understand his/her priorities.
Talk to your boss, make a two second statement like "I'm excited about Angular.js and I think it can help improve our business. However, rather than just pitching a technology to you, I'd like to learn more about your priorities and the priorities of our team so that I can focus my energies on improving our business."
Then sit back and listen.
Business priorities will trump a change in technologies. Also, if you want to be taken seriously, then you should know both the pluses and minuses of switching to Angular. What browsers do customer use? Are they supported? What is the skillset of the team? Will training be required? And so on. Be ready to discuss these topics objectively.
What benefits do you think Angular will bring? How will that help the company develop faster at a lower cost, provide a better user experience that'll increase revenue, etc.
