Consider the following quote from an advertisement for a home security company: "there's no price that can be placed on peace of mind. our advanced security systems will protect the well-being of your family so that you can sleep soundly at night." what rhetorical appeal is being used?

Before answering the question, I would like to present the different  modes of persuasion, also referred to as ethical strategies or rhetorical appeals. They are maneuvers in rhetoric that classify the speaker's appeal to the audience. The Rhetorical Appeals are:

Ethos: It is how well the presenter convinces the audience that the presenter is qualified to speak on the subject, and by doing that what the presenter says is valid.

Pathos: is an appeal to the audience’s emotions

Logos: it. It is normally used to describe facts and figures that support the speaker's claims or thesis.

Kairos: An orator uses this to their advantage to persuade the audience to act now at the time being

In this particular case the rhetoric appeal used is:

Pathos because the quote is trying to play with the emotions of the people using words like: well-being, security, peace of mind and family.

just took the test;

argument: "it's time to wage a war against britain to secure american freedom."

claims: "america has tried every peaceful method available for seperating from england" & "the americans' petitions to the king have been turned away by him."