ABCD is a square. Determine Angle DCA.

Given: A square ABCD

To Find: ∠DCA i.e., ∠2

Solution: We know all sides of a square are equal.

∴ AB = BC = CD = DA

So, in ∆ ACD, AD = CD

⇒ ∠2 = ∠1  (Angles opposite to equal sides are equal)

Now in ∆ ACD, by angle sum property of ∆,

∠ADC + ∠1 + ∠2 = 180°

⇒ 90° + 2 ∠2 = 180°  (Each angle of square = 90°)

⇒ 2 ∠2 = 180° – 90°

⇒ 2 ∠2 = 90°

⇒ ∠2 = 45°

Hence, ∠DCA = 45°.