It's a mistake to think that every question has an answer. It's an even bigger mistake to think that unanswerable questions aren't worth asking.
As I've said before, I see philosophy as an activity, or specifically, an activity of elucidating and clearing up confusion. Its task is to show that apparent problems are not, in fact, problematic, but merely pseudo-problems.
Thus, we divide questions (or problems) into two groups: those that can be answered and those that cannot.
The questions for which answers exist might belong to science, for example, where the search for these answers is central (or should be), or belong to our everyday practices. And those questions for which no answer exists are grouped under the term "nonsensical." For, to be clear, by "unanswerable questions," I don't mean paradoxes, such as the question of whether a barber shaves himself in Russell's Barber Paradox. Nor do I mean questions for which an answer theoretically exists, but is practically inaccessible (although it can be argued that the same applies to these questions). I do, however, mean questions that are logically unanswerable, in the sense that, if we were to formulate them differently, these questions would be patently nonsensical.
One might think that once we've labeled a question nonsensical, it's no longer worthy of our attention. But precisely those questions, to which there is no answer, are nevertheless absolutely worth asking. It's precisely these deeper questions where, even though seeking an answer is a Sisyphean task, we discover profound insights into life and ourselves by reflecting on them. (Something I somewhat confusingly still call "philosophizing").
While contemplating these questions, whether while taking a walk or relaxing in a large armchair, is a worthwhile activity, the sheer size and abstraction of the questions can be overwhelming and dissuasive. Fortunately, there is a medium where these questions can flourish: art.
Art is multifaceted, perhaps the most multifaceted there is, as multifaceted as humanity itself. We could consider art as a whole as one great project, an autobiography, or rather a diary, of the human soul. Not about what we have achieved, but about what we experience, how we feel, what we are struggling with. Art is where all our introspections reside, all our sorrows and loves, our emotions, desires, and beliefs. Together, humanity creates one great work of art, the work that will encompass everything about who we are.
(Should an intelligent extraterrestrial species ever come to Earth, we can display all of humanity's scientific knowledge and technological achievements to demonstrate what we are capable of, as if we were holding up our resumes. But if we want to introduce them to humanity personally, we should display all of our art.)
If we take a look at these unanswerable questions, we see that they penetrate these issues that often plague humanity. The unanswerable questions, even those stemming from epistemology or metaphysics, are essentially all questions of life philosophy.
And those are precisely the reflections on ourselves and our existence that we (among other things) try to express in art.
I love art very much; ultimately, I'd even dare to say that I can appreciate any art form and any art style, although I do, of course, have my own tastes and preferences. Music and literature (incl. poetry) are by far the art forms I consume most, but architecture and the visual arts also often garner my admiration (and video games, which I would consider art as well). However, there is one art form I accuse myself of not engaging with enough: film.
To be clear, I definitely watch a film from time to time, many times more often than I see some other art forms, such as theater. Yet, there is still so much film that I can gain a lot from.