We are given the following circle
First, we should label arc YZX. To do so, note that the measure of this arc is greater than the measure of arc YZW, which is an arc of 180°. So, the measure of arc YZW is greater than 180°. Thefore, it is a major arc.
To determine the measure of arc YZX, note that we only need the measure of arc YZ as we already know the measures of the other arcs. Note that as arc YZW has a measure of 180°. Then, the measures of arcs YZ and ZW should add up to 180°. This means that we have the following equation
[tex]arc\text{ YZ + 148=180}[/tex]
if we subtract 148 on both sides, we get
[tex]arc\text{ YZ=180-148=32}[/tex]
so we get the following graph
so, to find the measure of arc YZX, we add the measures of all arcs we already know their measure. So we get
[tex]arc\text{ YZX = 32+148+55=235}[/tex]
so the measure of arc YZX is 235°
