Question

$overleftrightarrow{hj}$ and $overleftrightarrow{jk}$ are tangent to $odot g$. what is $mangle j$?
$mangle j = square^circ$

Explanation:

Step1: Recall tangent-radius property

Tangents $\perp$ radii, so $\angle GHJ = 90^\circ$, $\angle GKJ = 90^\circ$.

Step2: Sum quadrilateral interior angles

Quadrilateral $GHJK$ has total interior angles $360^\circ$.

Step3: Calculate $\angle J$

$$m\angle J = 360^\circ - 90^\circ - 90^\circ - 120^\circ = 60^\circ$$

Answer:

$60^\circ$