The side BC of ΔABC is produced to D. The bisectors of ∠ABC and ∠ACD meet at E. If AB = AC and ∠BEC = 24°, then the measure of ∠ABC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 66°.
Let ∠ABC = ∠ACB = x
∠ECD = (180° - x)/2 = 90° - x/2
∠EBC = x/2
∠BEC = ∠ECD - ∠EBC
⇒ 24° = (90° - x/2) - (x/2)
⇒ 24° = 90° - x
⇒ x = 90° - 24° = 66°