Step-by-step explanation:
there is always the internet with good explanations.
1A
inner angle with vertex inside the circle :
x = sum(both outer angles)/2 = (47+116)/2 = 163/2 = 81.5°
1B
same thing as 1A, only that x is now the supplementary angle to the inner angle (that means the sum with the inner angle is 180°), because the inner angle and x are together the full sum of angles around one point on one side of a line.
the inner angle = (75+55)/2 = 130/2 = 65°
x = 180 - 65 = 115°
1C
now we need to do the reverse calculation.
we have the inner and one of the 2 outer angles.
the calculation is therefore
128 = (154 + x)/2
256 = 154 + x
x = 256 - 154 = 102°
