Angle Addition Postulate and Angle Bisectors

[missfunara]

If the measurement of angle ABC=28 and the measurement of angle ABD=53, find the measurement of angle CBD. (Find two possible answers.)

I know that one possible answer for the measurement of angle CBD is 25, but I can't seem to find another solution.
Thank you!

 

[stapel]

If the measurement of angle ABC=28 and the measurement of angle ABD=53, find the measurement of angle CBD. (Find two possible answers.)

Since we have no restrictions on the lengths of segments BC and BD, then the triangle ACD could be any triangle with m(angle CAD) = 81 degrees. As such, I see no way to narrow down "the answer" to only two possibilities. Sorry!

Eliz.

 

[pka]

There are two answers.
Case I. If points A & D are on opposite sides of \(\displaystyle \overleftrightarrow {BC}\) then ray \(\displaystyle \overrightarrow {BC}\) is between \(\displaystyle \overrightarrow {BA}\) and \(\displaystyle \overrightarrow {BD}\).
So \(\displaystyle m\left( {\angle DBA} \right) > m\left( {\angle CBA} \right) \Rightarrow \quad m\left( {\angle DBC} \right) = 25\).

Case II. If points A & D are on the same side of \(\displaystyle \overleftrightarrow {BC}\) then ray \(\displaystyle \overrightarrow {BA}\) is between \(\displaystyle \overrightarrow {BC}\) and \(\displaystyle \overrightarrow {BD}\).
So \(\displaystyle m\left( {\angle DBC} \right) = 81\).