Answer:
We know that the circle is divided into two equal parts by a diameter, and that the diameter is labeled “6” on both ends. This means that the diameter of the circle is 6 units long.
We also know that the arc labeled “AB” has a measure of 4π units. An arc is a part of the circle’s edge, and its measure tells us how long it is.
To find the measure of angle AOB, we can use a formula that relates the measure of an arc to the measure of its central angle. The formula is: arc measure = (angle measure / 360) * (2 * π * radius). Since we know the arc measure and the radius of the circle (which is half of the diameter), we can use this formula to find the angle measure.
Let’s plug in the numbers: 4π = (angle measure / 360) * (2 * π * 3). Solving this equation, we find that angle measure = 240.
So, the measure of angle AOB is 240 degrees.