The sum of all these angles is (180°+180°+90°)-(180°) = 270°. The explanation is that a and f are part of a 90 degree angle, while b,c and d,e are part of 180° angles. To all of them is subtracted an angle belonging to a triangle, whose angles sum to 180°.

We know in rectangle all angles are equal to 90 degree i.e angle r = angle s = angle t =angle u = 90 degree.

Now consider triangle RSX,

We have angle a + angle s +angle b = 180 degree

or angle a +angle b = 90 (since angle s = 90 degree)

Similarly in triangle XYT we have

angle c + angle d + angle t =180 degree

or angle c + angle d = 90 (since angle t = 90 degree)

and in triangle YRU

we have angle e +angle f + angle u =180 degree

or angle e + angle f =90 (since angle u = 90 degree)

Now putting the values in we get (a+b) +(c+d) + (e+f) = 90+90+90 = 270

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Triangle RSX: Angle S=90, hence Angle A+B=90
TRiangle XTY: Angle T=90, hence Angle c+d=90
Triangle YUR: Angle U=90, hence Angle e+f=90

A+B+C+D+E+F=90+90+90=270