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Question

In the above figure, ABCD is a square and BCE is an equilateral triangle. Find the measure of angle DEC.


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Solution

Given ABCD is a square and BCE is an equilateral triangle

BCD=90 [Interior angle of a square]

BCE=60 [Interior angle of an equilateral triangle]

DCE=90+60=150

BC = CD (Sides of a square) ------ (1)

BC = CE (Sides of an equilateral triangle) ------ (2).

From (1) and (2),
DC = EC

In ΔDCE, DC = CE
CDE=CED --------- (3) [Angles opposite equal sides]

Also, In ΔDCE
DCE+CDE+CED=180 --------- (4) [Angle sum property]

From (3) and (4),
2DEC+CED=180

2DEC=180150=30

DEC=12(30)=15

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