Good day, excuse me, I am looking at congruence themes in Geometry, and I am trying to solve this problem, but I am not sure how to proceed. The coloured numbers is what I have so far (although now looking at it, my angles could be wrong). Any help would be very much appreciated. Thanks!
Join $AB$. Then $AM=MB \Rightarrow \triangle AMB$ is equilateral.
Hence in $\triangle BAD$, $\angle BAD=60+30=90$ and $AD=AB$. Thus $\angle ADB = \angle ABD=45$.
Therefore the exterior $\angle X=\angle ADB + \angle DAM=75 $