(c) 45°
∠DCB = 90° (ABCD is a square)
∠TCB = 60° (DCT is an equilateral Δ)
∴ ∠DCT = 90° + 60° = 150°
DC = CB (Adj sides of a square)
CB = CT (Sides of an equilateral Δ)
⇒ DC = CT ⇒ ∠CTD =∠CDT (isos. Δ property)
In ΔDCT, ∠CTD = \(\frac12\) (180° –∠DCT)
= \(\frac12\) (180° – 150°) = 15°
∴ ∠BTD =∠BTC – ∠CTD= 60° – 15° = 45°.