Krispy Pizza, one of my local joints. Source.

This is a bit off-topic, but I saw Arcadia last night on Broadway, and it blew me away. I can’t stop thinking about it. If theater is your thing and tickets are within your means, then you should run and not walk. I still have chills. Even if theater is not your thing, it’s worth a read.

And now back to your regularly scheduled frustration. Prize this week: when you graduate and move to New York, the guy at your local pizza place will come to know you by first name and give you the biggest slice available whenever you come in. You will know, then, that you have made it.

In the figure above, the red lines divide the circle into 8 equal parts. What is z?

UPDATE: Nice work to John and Debbie, who both got this and who both will hopefully know the pleasure of being a regular at a local pizza joint one day, if they don’t already. Solution below the cut.

As is true in most geometry questions, it’s possible to solve for z in a number of different ways here. If your way was different than mine but you still got the same answer, that’s just fine. You say potayto, I say potahto.

First, recognize that if a circle is divided up evenly into 8 sections, then each of the central angles is going to be 360° ÷ 8 = 45°. Mark the ones that will probably matter for us:

Note that the triangle formed by the pink segments and the black one is isosceles, because the pink segments are both radii. That means, since the vertex angle is 135°, the other two must each be 22.5°.

We now have two of the three angles in the green triangle below, so we can solve for the third.

180° – 45° – 22.5° = 112.5°. Since the angle we’re looking for is vertical to that angle, z = 112.5 also.