Question

given ⊙o below, if (overarc{gh}) and (overarc{jk}) are congruent, what is the measure of (angle koj)?
a. (22^circ)
b. (158^circ)
c. (68^circ)
d. (112^circ)

Explanation:

Step1: Recall circle arc-angle rule

In a circle, congruent arcs correspond to congruent central angles.

Step2: Match congruent arcs to angles

Since $\widehat{GH} \cong \widehat{JK}$, their corresponding central angles $\angle GOH$ and $\angle KOJ$ are congruent.

Step3: Identify given angle value

We know $m\angle GOH = 68^\circ$, so $m\angle KOJ = m\angle GOH$.

Answer:

C. $68^\circ$