Question: In the diagram of circle $A$, what is the measure of $\angle XYZ$?
$\circ$ 35°
$\circ$ 70°
$\circ$ 75°
$\circ$ 140°
Circle $A$ diagram: a circle centered at $A$ with points $W$ (left), $Z$ (right), and $X$ (lower-left) on the circle; a vertical line through $Z$ and $Y$ extends downward to $Y$; a slanted secant from $W$ through $X$ continues to $Y$; arc $WZ$ is labeled 175° and arc $XZ$ is labeled 105°.
1. **Problem Statement:** We need to find the measure of $\angle XYZ$ in circle $A$ given arcs $WZ = 175^\circ$ and $XZ = 105^\circ$.
2. **Relevant Formula:** The measure of an angle formed by two secants intersecting outside a circle is half the difference of the intercepted arcs:
$$\angle XYZ = \frac{1}{2} |\text{arc } WZ - \text{arc } XZ|$$
3. **Calculate the difference of arcs:**
$$|175^\circ - 105^\circ| = 70^\circ$$
4. **Apply the formula:**
$$\angle XYZ = \frac{1}{2} \times 70^\circ = 35^\circ$$
5. **Conclusion:** The measure of $\angle XYZ$ is $35^\circ$.
This matches the first option.