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 =

Question

The side BC of &#x394; ABC is produced to a point D . The bisector of &#x2220; A meets side BC in L, If &#x2220; ABC = 30&#xB0; and &#x2220; ACD = 115&#xB0;, then &#x2220; ALC =

Philoid · Accepted Answer

Given,

∠ABC = 30^o

∠ACD = 115^o

By exterior angle theorem,

∠ACD = ∠A + ∠B

115^o = ∠A + 30^o

∠A = 85^o

∠ACD + ∠ACL = 180^o (Linear pair)

∠ACL = 65^o

In

∠ALC + ∠LAC + ∠ACL = 180^o

∠ALC + ∠A + 65^o = 180^o

∠ALC = 72.5^o

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 =