Question

question 1 of 10
what is the measure of (overarc{xyz})?
a. (196^circ)
b. (98^circ)
c. (278^circ)
d. (164^circ)

Explanation:

Step1: Recall inscribed arc theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, $\angle XYZ = 82^\circ$ is an inscribed angle intercepting arc $XZ$.

Step2: Calculate arc $XZ$

$\text{Arc } XZ = 2 \times \angle XYZ = 2 \times 82^\circ = 164^\circ$

Step3: Calculate arc $XYZ$

The total circumference of a circle is $360^\circ$. Subtract arc $XZ$ from $360^\circ$ to get arc $XYZ$.
$\text{Arc } XYZ = 360^\circ - 164^\circ = 196^\circ$

Answer:

A. $196^\circ$