Segments $ac$ and $bd$ are diameters of circle $O$. What is the measure of the angle formed by these diameters if the angle is greater than $180°$ and less than $360°$?

• A. $146°$
• B. $287°$
• C. $253°$
• D. $107°$

Answer: (C)

Verified step by step guidance

1. Understand that segments AC and BD are diameters of circle O, meaning both pass through the center O and each subtends a straight angle of 180° at the center.
2. Identify that the angle formed by these two diameters at the center O can be measured as the smaller angle between the two lines or the larger reflex angle, which is between 180° and 360°.
3. Note that the problem asks for the angle measure greater than 180° and less than 360°, so we are looking for the reflex angle between the two diameters.
4. If the smaller angle between the diameters is given or can be found (for example, 107°), calculate the reflex angle by subtracting this smaller angle from 360° using the formula: \$360^\circ - \text{smaller angle}$.
5. Apply this formula to find the reflex angle formed by the diameters, which will be the angle measure between 180° and 360° as required.