In circle $O$, $AB$ and $CD$ are diameters. Arc $ED$ measures $170°$. What is the measure of arc $AE$?

• A. $270°$
• B. $253°$
• C. $180°$
• D. $107°$

Answer: (B)

Verified step by step guidance

1. Identify that points A, B and C, D are diameters of circle O, meaning each pair divides the circle into two arcs of 180° each.
2. Since AB and CD are diameters, arcs AB and CD each measure 180°.
3. Given that arc ED measures 170°, recognize that arc ED is part of the circle and lies between points E and D on the circumference.
4. Use the fact that the total measure of the circle is 360°, and consider the arcs around the circle to express arc AE in terms of known arcs: for example, arc AE = 360° - (arc ED + arc AB or CD, depending on the position of E).
5. Set up the equation for arc AE using the known arc measures and solve for arc AE without calculating the final numeric value.