Q4. - Geometry

Question

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

                           $\stackrel{⏜}{ABD}$

Step-by-Step Solution

Answer

a. The measure of an arc $\stackrel{⏜}{ABD}$ is $180.$

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

 $\begin{array}{l}\angle AOD=\angle AOB+\angle BOC+\angle COD\\ {\text{ = 50}}^{\circ }+{80}^{\circ }+{50}^{\circ }\\ \text{ = }{180}^{\circ }\end{array}$      

       Since 

    $\begin{array}{l}m\stackrel{⏜}{ABD}=m\angle AOD\\ \text{ =180}\end{array}$   

Therefore, the measure of arc $ABD$ is $180.$