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∘
(1 mark)
BC = CD [Sides of a square] ------ (1)
BC = CE [Sides of an equilateral triangle] ------ (2).
From (1) and (2),
DC = EC
(1 mark)
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),
2∠DEC+∠CED=180∘
(1 mark)
⇒2∠DEC=180∘−150∘=30∘
∠DEC=12(30∘)=15∘
(1 mark)