Given the points $17°$, $75°$, $149°$, and $211°$ on a circle, what is the measure in degrees of the minor arc from $75°$ to $149°$?

• A. $286°$
• B. $149°$
• C. $74°$
• D. $58°$

Answer: (C)

Verified step by step guidance

1. Identify the given points on the circle as angles measured in degrees from a fixed reference point, typically the positive x-axis. Here, the points are at 17°, 75°, 149°, and 211°.
2. To find the measure of the minor arc from 75° to 149°, calculate the difference between these two angles: \$149^\circ - 75^\circ$.
3. Since the points lie on a circle, the arc measure corresponds to the central angle between these two points, which is the difference calculated in the previous step.
4. Verify that this difference represents the minor arc by checking if it is less than 180°. If it were greater than 180°, you would subtract it from 360° to find the minor arc.
5. Conclude that the measure of the minor arc from 75° to 149° is the difference found, which is less than 180°, confirming it is the minor arc.