Question

Find the measure of central $\angle 1.$

Short answer

The measure of angle $\angle 1$ is $55°.$

Step-by-step solution

Step 1. Given information:

The figure is given with the arc $=35°$

Step 2. Concept used:

In the circle the measure of arc is given.

$1)$The total angle corresponding to one full circle is $360°$

$2)$ A quadrant portion corresponds to $90°.$

Step 3. Applying the concept:

Here, we can see that in the figure.

Here, $\angle 1$ is a part of a quadrant whose other part is $35°.$Thus, the $\angle 1$ can be calculated as,

$\begin{array}{c}\angle 1={90}^{\circ }-{35}^{\circ }\\ ={55}^{\circ }\end{array}$

Therefore, the measure of the angle $\angle 1$ is $55°.$