Mathematics

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

$150^{o}$

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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Single Correct Medium Published on 09th 09, 2020
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