This diagram shows a convex polygon, what’s the value of v?
Please explain!

This is actually a great problem. When you first look at it you might feel a little disgust, then a little fear, and then confusion. What do you do?

Well when I saw this, I thought, "What if I was on the outside of this shape, and walked all the way around it?" Let's entertain this idea for a second. When I turn each corner, I would be going however many degrees to get to the next side. And when I finally arrive back where I started, I have gone one full turn, 360º. So if you think about it, that means adding all the exterior angles must give you 360º!  Now we can solve for v:

(2v - 4) + 63 + (2v - 1) + (v + 37) + 36 + 113 + (4v - 37) = 360

9v + 207 = 360

9v = 153

v = 17.

Isn't that pretty?

step-by-step explanation: