Let's draw the circle and the lines to see more clear:
The AB and CD are diameters of the circle, so the intersection point K is the center of the circle.
We know the angle BKD=100°, but the angle AKC=BKD because they are opposite angles.
So the measure of arc AC is:
[tex]\begin{gathered} \text{arc AC=}\angle AKC\cdot r \\ \text{where the r is the radius of the circle} \end{gathered}[/tex]
You should note the angle AKC in the above equation must be in radians. To convert degrees to radians use the following equation:
[tex]\angle AKC(radians)=\frac{\pi}{180}\angle AKC(degrees)[/tex]
So,
[tex]\text{arc AC=}\frac{\pi}{180}\cdot100\cdot r=\frac{5}{9}\pi\cdot r[/tex]
