Question

In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACD meet at E, then ∠E =

(a) 25°

(b) 50°

(c) 100°

(d) 75°

Answer 1

In the given figure, bisectors of and meet at E and

We need to find

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

In ΔABC with as its exterior angle

........(1)

Similarly, in with as its exterior angle

(CE and BE are the bisectors of and)

.......(2)

Now, multiplying both sides of (1) by

We get,

......(3)

From (2) and (3) we get,

Thus,

Therefore, the correct option is (a).