The Angles of a Roof

Date: 11/20/95 at 12:43:5
From: Anonymous
Subject: geometry

I am trying to build a model house but am having trouble with laying 
out the roof.  The main part of the house has a peaked roof (an "A" 
frame house); the angle formed when the roof meets the ground is 60 
degrees.

There is an addition onto the A-frame with a 30 degree angle formed to 
the walls.

     /\
    /  \------+
   /    \____/_\
  /      \   | |  
 /        \  | |    
             
What angle should the addition's roof be cut at so it meets the A-frame
roof?

Your help would be appreciated.

Ben Homan

Date: 12/19/95 at 15:14:13
From: Doctor Tarin
Subject: Re: geometry

Here's an answer. 

         A
        /\
       / E\------+F
      /    \____/_\
     /      \   | |  
    /________\__|_| 
   B          C   D

Angle ACB and angle ACD are supplements (they add up to 180 degrees). 
So if angle ACB is 60 degrees, angle ACD is 120 degrees.  There is a 
theorem in geometry that says that AEF and ACD are congruent (they have 
the same measure), so angle AEF is also 120 degrees.  Angle AEF and 
angle FEC are supplements, so angle FEC must be 60 degrees.  Cut that 
angle, and your roofs should meet.

-Doctor Tarin,  The Geometry Forum