Question

what is ( mangle jik )?
write your answer as an integer or decimal.
( mangle jik = square^circ )

Explanation:

Step1: Find arc JK measure

The central angle for arc $JK$ is supplementary to $143^\circ + 134^\circ$.
$$m\overset{\frown}{JK} = 360^\circ - 143^\circ - 134^\circ = 83^\circ$$

Step2: Apply inscribed angle theorem

$\angle JIK$ is an inscribed angle over arc $JK$, so its measure is half the arc's measure.
$$m\angle JIK = \frac{1}{2} \times m\overset{\frown}{JK}$$

Step3: Calculate final angle measure

Substitute the arc measure into the formula.
$$m\angle JIK = \frac{1}{2} \times 83^\circ = 41.5^\circ$$

Answer:

$41.5$