Question

Find arc IJ, I have been having trouble with this one...

Answer 1

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
`\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}`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,

`m\hat{IJ}=68(2)\text{ = 136}\degree`

Therefore, the answer is:

`m\hat{IJ}=136\degree`