Q4. - Geometry

Question

Find  the measure of central $\angle 1.$

Step-by-Step Solution

Answer

The measure of angle  $\angle 1$ is $50°.$

Step 1. Given information:

The given figure is,

Step 2. Concept used:

   In the circle the measure of arc is given.

   Opposite angles are equal and the arc is equal to the angle that is asked.

Step 3. Applying the concept:

  Here, we can see that in the figure.

Since both are vertically opposite angle so

Measure of arc  $\begin{array}{l}={180}^{\circ }-{130}^{\circ }\\ ={50}^{\circ }\end{array}$

  As we know,

                  $\angle 1=$ measure of arc

                    $=50°$

           

 Therefore, the measure of the angle $\angle 1$ is $50°.$