Side BC of a ΔABC is produced to D such that CD = AC. Also, AD = BD and AB = AC. What is the measure of ∠ADB?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 36°.
Let ∠ADC = ∠CAD = ∠ADB = x
∠ACB = Sum of the two internal angles is equal to the external angle = x + x = 2x
∠ABC = ∠ACB = 2x
In ΔABC, 2x + 2x + ∠BAC = 180°
⇒ ∠BAC = 180° - 4x
⇒ ∠BAD = 180° - 4x + x
If BD = AD then, ∠ABC = ∠BAD = 180° - 3x
In ΔABD, 180° - 3x + 180° - 3x + x = 180°
⇒ x = 36°