AoPSWiki
Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.

2007 AMC 12B Problems/Problem 11

From AoPSWiki

Solution

The angles in a quadrilateral add up to 360, regardless of what shape or size the figure takes. Let x be \angle A, so then:

\angle B=.5x

\angle C=(1/3)x

\angle D=(1/4)x

\angle A+\angle B+\angle C+\angle D=360

x+.5x+(1/3)x+(1/4)x=360

(25/12)x=360

x=172.8

or x is around 173, choice D.

See Also

2007 AMC 12B (ProblemsResources)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us