What are the formulas for angles inside or on a circle for their arcs

The video tutorial reviews three types of angles related to circles: central angles, inscribed angles, and angles formed by chords or secants. Central angles have their vertex at the circle's center, and their measure equals the arc's measure. Inscribed angles have their vertex on the circle, and their measure is half the arc's measure. Angles formed by chords or secants inside the circle are calculated as half the sum of the measures of the arcs they intercept.

What is the defining characteristic of a central angle in a circle?

• Its vertex is on the circle.

• Its vertex is outside the circle.

• Its vertex is at the center of the circle.

• Its vertex is on a chord.

If a central angle measures 70 degrees, what is the measure of its intercepted arc?

• 140 degrees

• 35 degrees

• 70 degrees

• 90 degrees

How is the measure of an inscribed angle related to its intercepted arc?

• It is unrelated to the arc.

• It is twice the arc.

• It is half the arc.

• It is equal to the arc.

If an inscribed angle measures 30 degrees, what is the measure of its intercepted arc?

• 90 degrees

• 30 degrees

• 15 degrees

• 60 degrees

What is the formula for finding the measure of an angle formed by two chords intersecting inside a circle?

• Half the difference of the intercepted arcs

• Half the sum of the intercepted arcs

• Equal to the intercepted arcs

• Twice the sum of the intercepted arcs