Angling for a Cookie

Find the angle, get a cookie. What could be a sweeter deal? The angle measurements refer to the angle along the circle. The figure is not to scale.
A = ?

Please submit your answer, along with your name and email address, to Professor Clay, Arter 104E. Solutions must be received by Friday, February 4th. All are invited to submit an answer, even Computer Science professors. All who submit a correct answer win FREE HOMEMADE COOKIES!! The student with the most correct answers at the end of the semester wins a copy of New Mathematical Diversions by legendary math puzzler Martin Gardner.

Mmmm... who can resist a FREE COOKIE?1

1 image found at: