Question

In ΔABC, D is point on BC such that AB = AD = BD = DC.
Show that: ∠ADC : ∠C = 4 : 1.

Answer 1

Since, AB = AD = BD
∴ ΔABD is an equilateral triangle.
∴ ∠ADB = 60°
⇒ ∠ADC = 180° − ∠ADB
               = 180° − 60°
               = 120°
Again in ΔADC,
AD = DC
∴ ∠1 = ∠2
But,
∠1 + ∠2 + ∠ADC = 180°
⇒ 2∠1 + 120° = 180°
⇒ 2∠1 = 60°
⇒  ∠1 = 30°
⇒  ∠C = 30°
∴ ∠ADC : ∠C = 120° : 30°
⇒  ∠ADC : ∠C = 4 : 1