How do I make a non-closed figure out of lines (continuous, because corners need to line up) of a certain thickness, and then cut it out?

Hi guys
Could you help me with this problem? I suspect it's very simple but I'm a beginner.
I need to create a continuous shape out of lines 15 pixels thick, and then cut it out. I've tried the line tool, using the shift key to add to endpoints, but then the corners do not end up exactly. I've also tried the path key on the pen tool, but this always closes the shape for me, which is not what I want. The shape IS the line.
I've attached a picture of a basic sketch of the shape I'd like to produce. Can any of you give me any advice? Thank you.

Draw a baseline guide to snap the pen tool to where you want the lines to line up If you're using CS6 or later, use the stroke so you can edit the line.

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How do I make a non-closed figure out of lines (continuous, because corners need to line up) of a certain thickness, and then cut it out?

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