Question

The side BC of ΔABC 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) $72\frac{1}{2}°$

(c) 145°

(d) none of these

Answer 1

In the given problem, BC of ΔABC is produced to point D. bisectors of meet side BC at L, and

Here, using the property, “exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,

In ΔABC

Now, as AL is the bisector of

Also, is the exterior angle of ΔALC

Thus,

Again, using the property, “exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,

In

Thus,

Therefore the correct option is (b).