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In the given diagram, ABCD is a square and ΔBCT is an equilateral triangle. ∠BTD equals

(a) 30° 

(b) 15° 

(c) 45° 

(d) 35°

1 Answer

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Best answer

(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°.

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