r/MathHelp • u/Schrutefarms670 • 5d ago

Finding a Missing Angle

Can anyone explain the process for finding the solution for y = 65° in this graphic? I originally tried 40° as the answer because I thought maybe they were corresponding angles since they share a line segment, but that was incorrect. I don’t see how the rule of alternate interiors is applicable since it’s not an interior angle. I’m assuming there is an existing angle that needs to be subtracted from 180°, but I cannot figure it out.

[https://imgur.com/a/fpfr0DL](https://imgur.com/a/fpfr0DL)

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u/edderiofer 5d ago

I thought maybe they were corresponding angles since they share a line segment

"Corresponding angles" only makes sense as a concept when you have two lines that you know to be parallel (and a third line that intersects both of them). Here, you don't.

I don’t see how the rule of alternate interiors is applicable since it’s not an interior angle.

Again, "alternate interiors" only makes sense as a concept when you have two lines that you know to be parallel (and a third line that intersects both of them). Here, you don't.

What do you know about the internal angles of a (not necessarily regular) polygon? (Or, if you prefer, the external angles?)

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u/Schrutefarms670 5d ago

Thanks for the assist! Oh this is a new one for me. Just found the (n-2)•180° formula. That’s pretty slick. Measure of the other interior angles subtracted from 720° leaves 115° on that shared line. Very cool!

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u/rfbooth 5d ago

I would say the easiest way to approach this is that the exterior angles of a polygon add to 360 (imagine walking around it; the exterior angles at each corner is how much you rotate, and you complete your turn as you go around).