∆ ABC is an equilateral triangle. The side BC is produced to point D. If A joines D and BC = CD, then the degree measure of angle CAD is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 30°.
According to the given question,
Since, BC = CD and BC = AC
Then AC = CD
Now, in triangle ABC, angle C = 60°
⇒ ∠ACD = 180° - 60°
∠ACD = 120°
Now in triangle ACD, ∠CAD = ∠CDA
⇒ ∠ACD + ∠CDA + ∠CAD = 180°
⇒ 120° + 2∠CAD = 180°
⇒ ∠CAD = 60°/2
⇒ ∠CAD = 30°