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Senior one math problem! How to do this problem when you kneel for a master in high school mathematics! Seek the detailed process. Ok, it will be adopted!
The key here is simplification.

β=90+k*360=90+2k* 180

See clearly that this is an even number (2k) times of 90 plus 180.

β= 270+k * 360 = 90+ 180+2k * 180

= 90+(2k+ 1) * 180 See clearly that this is 90 odd (2k+ 1) times of 180.

The union is an integer multiple of 90 plus 180.

So you get 90+n * 180, where n is an integer.

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