June 4th, 2010, 11:34 AM  #1 
Newbie Joined: Jun 2010 Posts: 3 Thanks: 0  Find an angle
Find the measure of the angle LDB. I'm looking for synthetic proof! 
June 4th, 2010, 01:38 PM  #2 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: Find an angle
angle DLB = 110 degrees. angle ALB = 70 degrees because the three angles in a triangle = 180 degrees, also because two sides of that triangle are congruent, so a theorem(forgot which one) says that the one unknown angle opposite the one congruent side also has the same angle measurement as the other angle opposite the other congruent side. angle LBD = 55 degrees because of the same reason above, except the congruent side is shared by both triangles, but same idea. angle LDB = 15 degrees because the interior angles of a quadrilateral = 360 degrees. Then angle DLB = 110 degrees because the three angles in a triangle = 180 degrees: 15 + 55 + 110 = 180. I don't know what you mean by synthetic proof, but this is the proof I can give you. 
June 5th, 2010, 01:18 AM  #3 
Newbie Joined: Jun 2010 Posts: 3 Thanks: 0  Re: Find an angle
you made a mistake. measure of the angle LDB is 23 degrees. 
June 5th, 2010, 08:16 AM  #4 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: Find an angle I see my mistake, sorry about that.

June 5th, 2010, 09:39 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
Angle LDB is approximately 22.93°. How much accuracy is expected? The tangent of the angle is 1/(2 + tan 20°), so I think the angle can't be found without using trigonometry. 
June 6th, 2010, 08:36 AM  #6  
Newbie Joined: Jun 2010 Posts: 3 Thanks: 0  Re: Quote:
 
June 6th, 2010, 10:35 AM  #7  
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Find an angle Quote:
 
June 6th, 2010, 11:26 AM  #8 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: Find an angle
I realized my mistake after OP told me I was wrong. That was kind of stupid of me to say because it didn't make sense after I read it again. I can tell you that I first thought it could be 55 degrees because the triangles shared the same side and the angle opposite that side was 55 degrees in one triangle, so I thought the other angle should also be 55 degrees. But then I realized you can't make those kinds of assumptions unless they're in the same triangle.

June 6th, 2010, 10:53 PM  #9 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Find an angle
Aha, I see. Thank you.


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