# The side BC of Δ ABC is produced to a point D. The bisector of ∠A meets side BC in L, If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC =A. 85°B. 72°C. 145°D. None of these

Given,

ABC = 30o

ACD = 115o

By exterior angle theorem,

ACD = A + B

115o = A + 30o

A = 85o

ACD + ACL = 180o (Linear pair)

ACL = 65o

In

ALC + LAC + ACL = 180o

ALC + A + 65o = 180o

ALC = 72.5o

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