what is the value of angle A The triangle ABC is random. The line $AD$ is twice big as the line $DC$ ($AD=2*DC$). We know only the two angles that are shown in the picture. What's the value of angle $A$?
If you only want the measure of the angle (and after deduce with a geometric/trigonometric procedure) Geogebra gives the following:
I think the correct is answer equal to $75°$

I did it by construction

First of all I made triangle $BDC$ with ur provided information and doing some calculations ie ($\measuredangle DBC=15°$, $\measuredangle BDC=120^{\circ}$ ,$\measuredangle BCD=45°$) than I continued line $CD$ till point $A$ with ur information ($2CD=AD$) as I got point $A$ , I joined it with $B$ and calculated $\measuredangle BAD$ which comes up to be $75°$