An Angle on Flashlights

Team: 
The Four -Sided Triangle
Topic: Plane Geometry
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Two friends decide to go camping together, but when one abandons the other and goes back home panic breaks out. So he must find the flashlight with the biggest angle to help him see better in the dark and hopefully help him find his friend faster.

Common Core Standards: 8.G.5
Problem #: 
137 (2013-2014)
Problem Difficulty Level: 4 [?]