December 6th, 2010, 07:45 AM  #1 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  X,Y angles. [color=#000000]Find the measure of the angles X and Y. [/color] [attachment=0:1m0lk1hg]angles.png[/attachment:1m0lk1hg] [color=#000000]Where ? put Y .[/color] 
December 7th, 2010, 01:43 PM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: X,Y angles.
Hello ZardoZ, I'm not sure on how to phrase in English, but I'll try: First we'll solve for X: The angles of the Pentagon are . constructing an isosceles triangle with top angle of gives a base angle of (The "baseline" is the lengthened line from M to . Now by using complementary angles, we have: Now for Y. Lengthen the line to the other pentagon intersecting the triangle in . Now, we have a triangle, B. So we have The angles of a hexagon are Angle M = Angle B (do you see that in the picture?) So Angle B = Now, angle Y Hoempa 
December 7th, 2010, 02:17 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,845 Thanks: 1567 
With "in ." changed to "in B." (which you probably intended) both calculations make sense and get the correct answers. The minimal annotation of the diagram makes it a bit awkward to explain things clearly. In particular, one needs to assume that the pentagons and hexagon are regular, so that their angles are known.

December 7th, 2010, 05:10 PM  #4 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: X,Y angles. [color=#000000]The answers are correct, I must have mentioned though that the pentagons and hexagon are regular.[/color] 
December 7th, 2010, 06:58 PM  #5  
Senior Member Joined: Nov 2010 Posts: 288 Thanks: 1  Re: X,Y angles. Quote:
 
December 7th, 2010, 07:59 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,845 Thanks: 1567 
I think Hoempa simply forgot to omit "/2", which doesn't belong in that line, but was needed in the earlier calculation.

December 8th, 2010, 11:46 AM  #7 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: X,Y angles.
What you say is correct, skipjack, I copypasted these calculations and forgot to eliminate "/2", and I see that I was to say "in B." I can't edit though. Glad, it made sense, afterwards. Hoempa 

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