Answer:
C. \(95^{\circ}\)
Step-by-step explanation:
Let x represent 4th angle of the given quadrilateral.
We have been that a quadrilateral has three angles that measure \(80^{\circ}\), \(110^{\circ}\) and \(75^{\circ}\). We are asked to find the measure of the fourth angle.
We know that all the interior angles of a quadrilateral are equal to 360 degrees, so we can set an equation as:
\(x+80^{\circ}+110^{\circ}+75^{\circ}=360^{\circ}\)
\(x+265^{\circ}=360^{\circ}\)
\(x+265^{\circ}-265^{\circ}=360^{\circ}-265^{\circ}\)
\(x=95^{\circ}\)
Therefore, the measure of 4th angle is 95 degrees and option C is the correct choice.
