Difference between revisions of "2007 AMC 10B Problems/Problem 7"
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Revision as of 17:07, 27 May 2011
Problem 7
All sides of the convex pentagon 
are of equal length, and 
What is the degree measure of 
Solution
![[asy] unitsize(1.5cm); defaultpen(linewidth(.8pt)+fontsize(10pt)); pair A=(0,2), B=(0,0), C=(2,0), D=(2+sqrt(3),1), E=(2,2); draw(A--B--C--D--E--cycle); draw(E--C,gray); draw(rightanglemark(B,A,E)); draw(rightanglemark(A,B,C)); label("$A$",A,NW); label("$B$",B,SW); label("$C$",C,SE); label("$D$",D,E); label("$E$",E,NE); [/asy]](http://latex.artofproblemsolving.com/b/1/a/b1adac4a39fceaa691b5d5346eee30cd5e1094fc.png)
because they are opposite sides of a square. Also, 
because all sides of the convex pentagon are of equal length. Since 
is a square and 
is an equilateral triangle, 
and 
Use angle addition
![\[\angle E = \angle AEC + \angle CED = 90 + 60 = \boxed{\textbf{(E)} 150}\]](http://latex.artofproblemsolving.com/7/6/7/7676dfaafe286eed98677436adb6d221a5797049.png)
