The side BC of ΔABC is produced to D. The bisectors of ∠ABC and ∠ACD meet at E. If AB = AC and ∠BEC = 35°, then the measure of ∠ABC will be:
Answer & explanation
Correct answer: option 2
We have,
AB = AC
∠BEC = 35°
= AB = AC
= ∠ACB = ∠ABC
We know,∠ACB + ∠ACD = 180° (linear angles)
=∠ACB = 180° - ∠ACD
=∠ACB = 180° - 2b
= 2a = 180° - 2b
= 2a + 2b = 180°
= a + b = 90°
In ΔBEC, exterior angle equal to sum of exterior angles.
=∠EBC + ∠BEC = ∠ECD
= a + 35° = b
= b - a = 35°
Solving,
= b = 62.5° and a = 27.5°
∠ABC = 2x = 2 × 27.5 = 55°