In the given figure, equilateral triangle $A E D$ is contained within square $A B C D$ . What is the degree measure of $∠ B E C$ ?

60^{o}

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100^{o}

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120^{o}

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150^{o}

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Solution

The correct option is D $150^{o}$
$s i d e s A D = A E = D E = A B = B C = C D$

$I n t e r n a l a n g l e o f s q u a r e = 90^{0}$

$A S, ∠ D A E = 60, t h e n ∠ B A E = 30^{0}$

$A E = B A, a n g l e o p p o s i t e t o t h e m a r e e q u a l$

$I n Δ A E B \Rightarrow 30 + x + x = 180 \Rightarrow x = 75 = ∠ A E B$

$I n Δ D E C \Rightarrow 30 + x + x = 180 \Rightarrow x = 75 = ∠ D E C$

$∠ A E D + ∠ D E C + ∠ A E B + ∠ B E C = 360$

$60 + 75 + 75 + ∠ B E C = 360$

$∠ B E C = 150$

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