The image shows a circle divided into sectors. We are given the degree measures of three sectors: $75^\circ$, $110^\circ$, and $110^\circ$. We need to determine the measure of the central angle of the remaining sector, labeled 'A'.

1. Problem Description

The image shows a circle divided into sectors. We are given the degree measures of three sectors: $75^\circ$, $110^\circ$, and $110^\circ$. We need to determine the measure of the central angle of the remaining sector, labeled 'A'.

2. Solution Steps

The sum of the central angles of all sectors in a circle is $360^\circ$. Let $x$ be the measure of the central angle of sector A.

We can write the equation:

$x + 75 + 110 + 110 = 360$

$x + 295 = 360$

$x = 360 - 295$

$x = 65$

3. Final Answer

The measure of the central angle of sector A is $65^\circ$.