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Geometry
Level
4
In the figure , AB = BC = CD = CD = DE = EF = FG = GA
Then measure of angle DAE (in degrees) is approximately :
The answer is 25.
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1 solution
Given conditions leads to a conclusion that (Angle DAE) = (Angle EDC) ; (Angle CDA) = (Angle CBD) = 2 (Angle DAE) ; (Angle EDA) = 3 (Angle DAE) ; (Angle DEA) = (180 - (Angle EDC))/2 = 90 - (Angle DAE)/2 . Now, Since sum of all angle of a triangle equals 180 degrees, Hence, (Angle DAE) + (Angle DEA) + (Angle EDA) = 180 ; => (Angle DAE) + 90 - (Angle DAE)/2 + 3 (Angle DAE) = 180 ; => (Angle DAE) = 90 2/7 =180/7 = 25.714 degrees. :)