Question

Find the measure of central $\angle 1.$

Short answer

The measure of angle $\angle 1$is $52°.$

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.

We calculate the asked angle subtracting the addition of its given measures of arcs from the total degree of the circle.

Step 3. Applying the concept:

Here, we can see that in the figure.

Since both are vertically opposite angle so

Measure of arc$\begin{array}{l}={360}^{\circ }-({240}^{\circ }+{68}^{\circ })\\ ={360}^{\circ }-{308}^{\circ }\\ ={52}^{\circ }\end{array}$

As we know,

$\angle 1=$measure of arc

$=52°$

Therefore, the measure of the angle $\angle 1$is $52°.$