The measure of angle ACF is 96°
Angles on a straight line add up to 180 degrees. When two lines intersect, opposite angles are equal.
This geometric principle, based on the linear pair postulate, is fundamental in understanding angles formed by intersecting lines.
90 + 38 + angle PCB = 180
angle PCB = 180 -128 = 52°
angle ACH = 52( opposite angles)
Therefore;
52+ 6x + 2x = 180
8x = 128
x = 16
Therefore angle ACF = 6x = 6 × 16 = 96°