In Act I Scene 1 do you think Egeus is justified in being angry with his daughter? Why or why not?
The answer to this question is wholly dependent on perspective. In the eyes of the law, Hermia is Egeus' daughter, therefore she is his property until he hands her off to a husband. As such, he is allowed to do with her as he wishes and she is not to have any say in the matter. However, from a modern perspective, we view this as repressive and controlling behavior because, as an American society, we do not accept the concept of arranged marriages. It is important, however, to acknowledge that some cultures do still view arranged marriages as the norm, so again the potential justification for his anger is largely dependent on the reader.
Hermia has defied her father. We do accept that children should not defy their parents as long as their parents requests or demands are reasonable. The question, then, is is Egeus' demand that Hermia marry Demetrius reasonable?
This is a matter of perspective, but it can also be argued that Shakespeare, given his resolution in this work as well as his tragic outcome in Romeo and Juliet, had his own opinions about parental involvement in their children's relationships. From the writer's perspective, therefore, it is arguable that his anger is not justified.
By our standards today, no, Egeus should not be angry with his daughter. But by the standards of the times in which Shakespeare wrote, he absolutely does.
Egeus wants Hermia to marry Demetrius. She wants to marry Lysander. He is angry at her and orders her to obey.
Back in those days, this was perfectly reasonable. Marriages (especially between important people) were generally not about love. Instead, parents picked spouses for their children based on what that spouse could do for the family. This usually meant that they picked spouses who could help the family with better business connections or more social status or something like that.
So Egeus absolutely had the right to be angry.