The Trick for Finding Interior Angles of Wonky* Shapes

Can you find x?

 

My students know if they can figure out this angle, they’ll be able to solve for x (by finding their way around the geometry section in 180 degrees.)

But here they get stumped. How do you figure out how many interior degrees there are in wonky shapes?

180 degrees comes to the rescue, again!

If only it were a triangle! Which we know has 180 degrees in it.

Can we chop it up into triangles? (Start at one point on the shape and draw lines out from that point. You are trying for the minimum number of triangles.)

 

Aha! So there are three triangles. Therefore, there are 180 x 3 = 540 degrees in this shape.

 

 

 

 

 

 

To find any particular angle, divide the total degrees by the number of angles: 540/5 = 108.

Since this angle is 108, and we know there are 180 degrees in a straight line, x must be 180-108 = 72.

 

 

 

 

 

 

*Wonky being anything that isn’t a triangle, btw.