Question

Find the measure of central $\angle 1.$

Short answer

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

Step-by-step solution

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 $50°.$