Q3. - Geometry

Question

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

  $\stackrel{⏜}{AC}$

Step-by-Step Solution

Answer

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

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 $130.$