Given:
Measure of arc LV = 56 degrees
Measure of arc JR = 146 degrees
Let's find the measure of angle 1.
To find the measure of angle 1, apply the angle arc relationship.
Let's first find the measure of arc JL and VR.
Measure of arc JL and VR = 360 - 56 - 146 = 158 degrees.
Hence, to solve for angle 1, we have:
[tex]m\angle1=\frac{arcJL+arcVR}{2}[/tex]
Where:
arcJL + arcVR = 158 degrees.
Thus, we have:
[tex]\begin{gathered} m\angle1=\frac{158}{2} \\ \\ m\angle1=79^o \end{gathered}[/tex]
Therefore, the measure of angle 1 is 79 degrees.
ANSWER:
79°
