Question

Find the measure of central $\angle 1.$

Short answer

a. The measure of angle $\angle 1$ is $80°.$

Step-by-step solution

Step 1. Given information:

The given figure is,

Step 2. Concept used:

In the circle the angle of the circle can be calculated by subtracting the total angle of the circle by its given value.

Step 3. Applying the concept:

Here, we can see that in the figure.

Measure of arc,

$\begin{array}{l}={360}^{\circ }-{280}^{\circ }\\ ={80}^{\circ }\end{array}$

As we know,

$\begin{array}{l}\angle 1=\\ \text{=}{80}^{\circ }\end{array}$ measure of arc

Therefore, the measure of the angle $\angle 1$ is $80°.$