Question

a is the center of the circle. classify each angle of a circle. write the angle names with three capital letters and no spaces.

inscribed angle \\(\angle\\)
circumscribed angle \\(\angle\\)
central angle \\(\angle\\)

Explanation:

Identify the inscribed angle

An inscribed angle has its vertex on the circle and sides that are chords of the circle. Looking at the diagram, vertex \(F\) lies on the circle, and chords \(FK\) and \(FJ\) form the angle:

$$ \angle KJF \text{ or } \angle JFK $$

Since \(K\), \(L\), and \(F\) are collinear on chord \(KF\), the angle is:

$$ \angle JFK $$

Identify the circumscribed angle

A circumscribed angle has its vertex outside the circle, and its sides are tangent to the circle. Vertex \(I\) lies outside the circle, with tangent lines \(IF\) and \(IG\) meeting at \(I\):

$$ \angle FIG $$

Identify the central angle

A central angle has its vertex at the center of the circle. Since \(A\) is the center, the angle formed by radii \(AD\) and \(AE\) is:

$$ \angle DAE $$

Answer:

A is the center of the circle. Classify each angle of a circle. Write the angle names with three capital letters and no spaces.

Inscribed Angle \(\angle\) <blank>JFK</blank>

Circumscribed Angle \(\angle\) <blank>FIG</blank>

Central Angle \(\angle\) <blank>DAE</blank>