Q6 of 28 Page 95

In the figure, AB = BC = CD, ∠A = xo. Prove that ∠DCF = 3∠A.

Given: AB = BC = CD and ∠ A = x°


To Prove: ∠ DCF = 3 ∠ A


Proof:


In Δ ABC


AB = BC [Given]


∴ ∠ A = ∠ C = x°


Now,


∴ ext. ∠ B = ∠ A + ∠ C


⇒ Ext. ∠ B = x° + x°


⇒ Ext. ∠ B = 2x°


In Δ CBD


BC = CD [Given]


∴ ∠ B = ∠ D = 2x°


Now,


In Δ ADC,


Ext. ∠ DCF = ∠ CDA + ∠ CAD


⇒ ∠ DCF = 2x + x


⇒ ∠ DCF = 3x


⇒ ∠ DCF = 3 ∠ A [ ∠ A = x°, Given]


Hence Proved.


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