Question

In exercises $2-7$ find the measure of the arc.

role="math" localid="1649086294011" $\stackrel{⏜}{AC}$

Short answer

a. The measure of an arc $\stackrel{⏜}{AC}$ is $130.$

Step-by-step solution

Step 1. Given information:

The given figure is,

Step 2. Concept used:

Following properties are used here,

The arc length of a circle can be calculated with the radius and central angle.

Step 3. Applying the concept:

Here, in the figure

$\begin{array}{l}\angle AOC=\angle AOB+\angle BOC\\ {\text{=50}}^{\circ }+{80}^{\circ }\\ \text{=}{130}^{\circ }\end{array}$

Since

$\begin{array}{l}m\stackrel{⏜}{AC}=m\angle AOC\\ \text{=130}\end{array}$

Therefore, the measure of arc $AC$ is $130.$