Responses to PUZZLE #38 What is the angle?

Given: triangle ABC, where line BD bisects <B, and the length of AD equals that of BD and also BC, find the size/measure of angle A, m<A.

From the given we see that triangles ABD and BCD are isosceles. This means that m<A = m<ABD, and m<C = m<CDB.

Also, from the given we know m<B = 2m<A = 2m<ABD.

Now notice that m<CDB = m<A + m<ABD by the exterior angle Theorem (or, if you prefer, m<CDB = 180 - m<ADB, and m<ADB = 180 – (m<A+m<ABD))?

Using this info plus the result that the measure of the angles of a triangle always equals 180deg. should give you the result.