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The sum of angles in the upper quadrilateral is 360 degrees. The top one must be 60 degrees. Beta and Gamma add up to 180 degrees. That leaves the desired 120 degrees. The only missing step is why beta and gamma add up to 180.
Something like that?
Not quite right but the solution is that ‘simple’.
My answer:
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Nice! I'd add a little argument why the two angles you denote by theta are equal.
Ok. Angles 1 and 2 summed together obviously = 180 degrees, but then so do 2 and 3.
If 1+2=180, and 1+3=180, then 2=180-1 and 3=180-1 so 1 and 3 are equal.
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