Mathematics

In the given figure, equilateral triangle $$AED$$ is contained within square $$ABCD$$. What is the degree measure of $$\angle BEC$$?


ANSWER

$$150^{o}$$


SOLUTION
$$ \displaystyle  sides\,AD = AE = DE = AB =BC = CD $$

$$  \ Internal \, angle \, of \,  square = 90^0 $$

$$ AS, \angle DAE = 60, then \angle BAE = 30^0 $$

$$ AE = BA, angle\,opposite \,to \,them \,are \,equal $$

$$ In\ \Delta AEB \Rightarrow 30 + x + x = 180 \Rightarrow x = 75 = \angle AEB $$

$$ In\ \Delta  DEC \Rightarrow 30 + x + x = 180 \Rightarrow x = 75 = \angle DEC $$

$$ \angle AED +\angle DEC +\angle AEB +\angle BEC = 360 $$

$$ 60 +75 +75+ \angle BEC = 360 $$

$$ \angle BEC = 150 $$ 
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