Question

A toy car races along a circular track and is constantly 4 feet from the center of the race track. Imagine an angle with a vertex at the center of the race track that subtends the car's path. What is the measure of this angle?

1) 90 degrees
2) 180 degrees
3) 270 degrees
4) 360 degrees

Answer 1

The measure of the angle with a vertex at the center of the race track that subtends the car's path is 360 degrees.

Step-by-step explanation:

The measure of the angle with a vertex at the center of the race track that subtends the car's path can be determined using the concept of arc length. The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this case, the car's path is 4 feet from the center of the race track, so the radius of the circle is 4 feet.

For one complete revolution, the rotation angle is equal to the arc length of the path. In this case, since the car is constantly 4 feet from the center of the track, the arc length is equal to the circumference of the circle, which is 2πr = 2π(4) = 8π feet.

Now we can calculate the angle using the relationship between arc length and circumference: A = (arc length / circumference) * 360 degrees. Plugging in the values, we get A = (8π/8π) * 360 degrees = 360 degrees.

Therefore, the measure of the angle is 360 degrees.