Question

which circle has a central angle that measures 40°?

Explanation:

Step1: Recall the definition of a central angle

A central angle is an angle whose vertex is at the center of the circle.

Step2: Analyze each circle

• In the first circle, the \(40^{\circ}\) angle is an inscribed angle (vertex \(X\) is on the circumference, not the center \(U\)).
• In the second circle, the \(40^{\circ}\) angle has its vertex at the center \(U\) of the circle. So, it is a central angle.
• In the third circle, the \(40^{\circ}\) angle is formed by a tangent - secant (vertex \(Z\) is outside the circle, not at the center \(U\)).

Answer:

The second circle (the one with the \(40^{\circ}\) angle having its vertex at the center \(U\) of the circle) has a central angle that measures \(40^{\circ}\).