Question about Snell's law and angle of deviation

[John982]

This isn't even a homework question but in my textbook there is an example on how to find the angle of deviation in a prism. I understand how they got all the angles listed in the picture but what I cannot understand is how the angle of deviation can be found from 70 - 12 = 58 degrees (answer in the books example). It's probably a simple issue with my geometry but I'm having trouble figuring it out and the book isn't too clear. Thanks.
http://imageshack.us/photo/my-images/43/33528972.jpg/

 

[PeterO]

In my textbook there is an example on how to find the angle of deviation in a prism. I understand how they got all the angles listed in the picture but what I cannot understand is how the angle of deviation can be found from 70 - 12 = 58 degrees (answer in the books example). It's probably a simple issue with my geometry but I'm having trouble figuring it out and the book isn't too clear. Thanks.

http://imageshack.us/photo/my-images/43/33528972.jpg/

The exterior angle of a triangle is equal to the sum of the two interior, opposite angles.

D is the exterior angle to the triangle in the middle of the prism.

The left hand angle is 20^o [40^o + 30^o + X^o = 90^o]
The right hand angle is 50^o - 12^o

so 20^o + 50^o - 12^o → 70^o - 12^o = 58^o

 

[John982]

I knew it was just me forgetting a geometry rule. Thank you for your help.