Given:
Line GH is tangent to the circle at I.
To determine the measure of arc IJ, we first note that GH is a straight line so the angle is 180°. Hence, we can get the m[tex]\begin{gathered} m\angle JIH+m\angle JIG=180 \\ 112+m\angle JIG=180 \\ Simplify\text{ and rearrange} \\ m\angle JIG=180-112 \\ m\angle JIG=68\degree \end{gathered}[/tex]Next, we also note that when the vertex of the angle is on a circle, the measure of angle is half the measure of its intercepted arc. Hence,
[tex]m\hat{IJ}=68(2)\text{ = 136}\degree[/tex]
Therefore, the answer is:
[tex]m\hat{IJ}=136\degree[/tex]
