Question

ABCD is a square. Determine angle DCA

Answer 1

Solution:-

Square = ABCD (Given)
Let the angles in triangle ACD are ∠1 = A, ∠C = 2 ∠D = 3
As we know that all the sides of a square are equal.
Therefore,
AB = BC = CD = DA
In Δ ACD, AD = CD
⇒ ∠1 = ∠2 (Angles opposite to equal sides are equal)
Now, In Δ ACD, 
∠ADC + ∠A + ∠C = 180° (Angle sum property)
⇒ 90° + ∠A + ∠C = 180°
⇒ ∠A + ∠C = 180° - 90°
⇒ ∠A + ∠C = 90°
As both are equal, so
90°/2
= 45°
∠A = ∠C = 45°
Hence, ∠ DCA = 45°