January 16th, 2015, 04:13 PM  #1 
Newbie Joined: Jan 2015 From: Florida Posts: 1 Thanks: 0  Finding angles
I'm trying to find the 4 angles that are circled in the image. I need to make these cuts, but don't know how to find the angle. Any help is appreciated. 
January 16th, 2015, 07:11 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Top 2 angles are equal, so are bottom 2 angles (else no solution possible). Extend upwards until a triangle is formed. Let height of the triangle = 52+h. Then, by similarity: h / (119/16) = (h + 52) / 27 ; note that 1/2(14 7/8) = 119/16 Solve for h. Then use Law of Sines to calculate angles. 
January 17th, 2015, 05:36 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Btw, if you're not familiar with the stuff I've used, but simply want a way to "cut properly", then draw your diagram to scale (use graph paper), and simply measure the angles. 
January 17th, 2015, 12:29 PM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
Slightly modified the image; Observe that angle ADC + angle DAE = 180 degrees. Alternative method, construct DE such thet DE is perpendicular to AB (and CD). Now, AE is (27''14.875'')/2 and we have a right triangle with known sides so we can find the angles. 

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