Justin Trudeau uses a variety of methods to engage the audience in his speech "Remarks by Prime Minister Justin Trudeau to apologize to LGBTQ2 Canadians".
First of all, he adapts a style of writing that mixes highly formal and deeply personal words and phrases, which helps him create a speech that sounds properly official, but still reflects the emotional sensitivities of the topic.
Secondly, he makes efficient use of a range of rhetorical devices to make his speech both convincing and memorable, such as strategic applications of repetition and direct references.
Thirdly, he draws upon all three forms of appeal, making sure his speech is both rationally convincing (logos) and emotionally affecting (pathos), while also making himself appear as a trustworthy authority on the subject (ethos).
Finally, he uses a mix of direct and indirect argumentation to make the extent of the Canadian government's past crimes clear, thereby also making the case that an apology is both proper and necessary.