Use the diagram and angle measures to answer the question. angle VWX=62^circ angle WVX=78^circ angle WXY=106^circ not drawn to scale What is the measure of angle YXZ A. 34^circ B. 40^circ C. 74^circ D. 78^circ

To find the measure of \(\angle YXZ\), we need to use the given angle measures and the properties of angles in a plane.Step 1: Identify the relationship between the given angles.We have three angles given:- \(\angle VWX = 62^{\circ}\)- \(\angle WVX = 78^{\circ}\)- \(\angle WXY = 106^{\circ}\)Step 2: Find the measure of \(\angle VXY\).Since \(\angle VWX\) and \(\angle WVX\) form a linear pair with \(\angle VXY\), their sum should be equal to \(180^{\circ}\) because they are supplementary. Therefore, we can calculate \(\angle VXY\) as follows:\[\angle VXY = 180^{\circ} - (\angle VWX + \angle WVX)\]\[\angle VXY = 180^{\circ} - (62^{\circ} + 78^{\circ})\]\[\angle VXY = 180^{\circ} - 140^{\circ}\]\[\angle VXY = 40^{\circ}\]Step 3: Find the measure of \(\angle YXZ\).Now, we know that \(\angle WXY\) and \(\angle YXZ\) form a linear pair with \(\angle VXY\), so their sum should also be equal to \(180^{\circ}\). We can calculate \(\angle YXZ\) as follows:\[\angle YXZ = 180^{\circ} - \angle WXY\]\[\angle YXZ = 180^{\circ} - 106^{\circ}\]\[\angle YXZ = 74^{\circ}\]Therefore, the measure of \(\angle YXZ\) is \(74^{\circ}\), which corresponds to option C. \(74^{\circ}\).