Question

question 10 of 10 given ⊙o below, if $overparen{ab}$ and $overparen{cd}$ are congruent, what is the measure of ∠cod? a. 110° b. 20° c. 70° d. 290°

Explanation:

Step1: Recall circle - arc property

In a circle, if two arcs are congruent, then the central angles that intercept them are congruent.

Step2: Identify the central - angle relationship

Since $\widehat{AB}$ and $\widehat{CD}$ are congruent, and $\angle AOB$ is the central angle for $\widehat{AB}$ and $\angle COD$ is the central angle for $\widehat{CD}$, we have $\angle AOB=\angle COD$.

Step3: Determine the measure of $\angle AOB$

From the figure, $\angle AOB = 70^{\circ}$.

Answer:

C. $70^{\circ}$