The formula to find the arc length if the angle has been measured in degrees is
[tex]\text{ arc length }=\frac{\theta}{360\text{\degree}}\cdot2\pi r[/tex]
So, for the arc AB, you have
[tex]\begin{gathered} \theta=135\text{\degree} \\ r=5\operatorname{cm} \\ \text{ arc length AB }=\frac{135\text{\degree}}{360\text{\degree}}\cdot2\pi(5cm) \\ \text{ arc length AB }=\frac{135}{360}\cdot10\pi cm \\ \text{ arc length AB }=\frac{15}{4}\pi cm \end{gathered}[/tex]
Now, for the arc ACB, you have
[tex]\begin{gathered} \theta=360\text{\degree}-135\text{\degree}=225\text{\degree} \\ r=5\operatorname{cm} \\ \text{ arc length ACB }=\frac{225\text{\degree}}{360\text{\degree}}\cdot2\pi(5cm) \\ \text{ arc length ACB }=\frac{225}{360}\cdot10\pi cm \\ \text{ arc length ACB }=\frac{25}{4}\cdot\pi cm \end{gathered}[/tex]
Finally, if you add the arc lengths and leave this sum in terms of π, you have
[tex]\begin{gathered} \text{ arc length AB + arc length ACB }=\frac{15}{4}\pi cm+\frac{25}{4}\cdot\pi cm \\ \text{Circumference }=(\frac{15}{4}+\frac{25}{4})\pi cm \\ \text{Circumference }=(\frac{15+25}{4})\pi cm \\ \text{Circumference }=\frac{40}{4}\pi cm \\ \text{Circumference }=10\pi cm \end{gathered}[/tex]
Therefore, if you add the length of the minor arc AB and the length of the major arc ACB, you get the circumference of the circle, whose measure is
[tex]10\pi cm[/tex]
