If two diameters of a $\mathrm{circle}$ intersect to form an $\mathrm{angle}$ at the center, what is the measure of the $\mathrm{angle}$ formed between them?

• A. $100°$
• B. $50°$
• C. $120°$
• D. $80°$

Answer: (C)

Verified step by step guidance

1. Understand that diameters of a circle are straight lines passing through the center, dividing the circle into two equal halves.
2. Recall that the angle formed at the center by two intersecting diameters is the angle between the two straight lines originating from the center.
3. Since each diameter is a straight line, the angle between two diameters can be found by considering the angle between their corresponding radii (half of each diameter) or by using the fact that the full circle measures 360 degrees.
4. Use the property that the sum of angles around a point is 360 degrees, and if the two diameters form an angle \( \theta \), then the opposite angle formed by the other two halves of the diameters is \( 180^\circ - \theta \).
5. Apply the given information or use geometric reasoning to determine the measure of the angle formed between the two diameters, which is the angle at the center where they intersect.