Why were the colonists angered at the king's response to the Olive Branch Petition

While George III did not respond to the Olive Branch Petition, he did react to the petition by declaring his own Proclamation of Rebellion. This document, issued August 23, 1775, declared certain elements of the American colonies in a state of “open and avowed rebellion”.

Explanation:

to act quickly in times of danger to the united states

because you have to act quickly if you want to live/survive.

freedom of speech is also protected by the 1 amendment.

explanation:

here is pretty much what the 1st amendment says:

congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.