Angles and their 360-related angles

Question

Is there any name for two angles, where the second can be obtained using first. Eg: 100 and 60. We get 60 if we keep moving 100 degrees upto 1500 (1500 % 360 = 60). But 100 and 70 is not a matching pair. How do we find if two angles are a matching pair as per the above logic?

Answer 1

The congruence $ax\equiv b \pmod m$ is solvable for $x$ iff $\gcd(a,m) | b$.

Since $\gcd(360,100)=20$ there are solutions if $b$ is a (integer) multiple of $20$ as in your first case with $b=60,$ but $70$ is no multiple of $20$.

I do not know a special name for the solutions.