Question

question 10 of 10 given ⊙o below, the arcs ⌢wx and ⌢yz must be congruent. a. true b. false

Explanation:

Step1: Recall arc - congruence theorem

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

Step2: Identify central angles

The central angle for arc $\overset{\frown}{WX}$ is $\angle WOX$ and for arc $\overset{\frown}{YZ}$ is $\angle YOZ$. Given that $\angle WOX = 27^{\circ}$ and $\angle YOZ=27^{\circ}$, so $\angle WOX\cong\angle YOZ$.

Step3: Determine arc congruence

Since the central angles are congruent, by the arc - congruence theorem, $\overset{\frown}{WX}\cong\overset{\frown}{YZ}$.

Answer:

A. True