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 angle is at a point on the circumference (not the center), so it is not a central angle.
• In the second circle, the angle is at a point on the circumference (not the center), so it is not a central angle.
• In the third circle, the vertex of the \(40^{\circ}\) angle is at the center \(U\) of the circle. So this is a central angle.
• In the fourth circle, the angle is formed by a tangent - secant (not a central angle as the vertex is not at the center).

Answer:

The third circle (the one where the vertex of the \(40^{\circ}\) angle is at the center \(U\) of the circle)