Question

find the measure of the arc or angle indicated (include degree symbol)

Answer 1

Angle ZXY inscribes the arc ZY, so we can use the following relation to calculate the measure of arc ZY:

$\begin{gathered} <\text{ZXY}=\frac{1}{2}ZY \\ 85=\frac{1}{2}ZY \\ ZY=170\degree \end{gathered}$

Now, to find the measure of arc XZ, we can add all arcs and make the sum equal to 360° (complete circle):

$\begin{gathered} XZ+XY+ZY=360 \\ XZ+105+170=360 \\ XZ+275=360 \\ XZ=360-275 \\ XZ=85\degree \end{gathered}$