Question

what are the measures of $overset{\frown}{jk}$ and $angle kij$?
measure of $overset{\frown}{jk}$ = $square^circ$
measure of $angle kij$ = $square^circ$
in the circle: $angle jki=70^circ$, the measure of arc $ki$ is $116^circ$

Explanation:

Step1: Find measure of $\overset{\frown}{JK}$

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle KIJ$ intercepts $\overset{\frown}{JK}$, but first use the given arc $\overset{\frown}{KI}=116^\circ$. Wait, correct: The inscribed angle over arc $JI$ is $\angle JKI=70^\circ$, so arc $JI=2\times70^\circ=140^\circ$. The total circle is $360^\circ$.
$$360^\circ - 140^\circ - 116^\circ = 104^\circ$$
This is $\overset{\frown}{JK}$.

Step2: Find measure of $\angle KIJ$

$\angle KIJ$ is an inscribed angle intercepting $\overset{\frown}{JK}$. The measure is half the arc.
$$\angle KIJ=\frac{1}{2}\times104^\circ=52^\circ$$

Answer:

Measure of $\overset{\frown}{JK}$ = $104^\circ$
Measure of $\angle KIJ$ = $52^\circ$