Question

if the the given figure AB AND BC ATE THE TANGENT AT A AND C RESPECTIVELY TO THE CIRCLE WITH THE CENTRE O FIND ANGLE ABC IF ANGLE AEC IS 105 DEGREE​

Answer 1

Step-by-step explanation:

AB = AC, hence ∠ABC = ∠ACB (∵ Two sides of a triangle are equal then, opposite angles are also equal)

∠ACB + ∠ACD = 180° (Linear Pairs sum = 180°)

∠ACB = 180° - 105° = 75° (∵ ∠ACD = 105° )

As ∠ABC = ∠ACB

∴ ∠ACB = 75°

In triangle ABC:

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 75° + 75° + ∠BAC = 180°

∴ ∠BAC = 180° - 150° = 30°