Angles in Circles

Front

What is the definition of an angle in a circle?

Back

An angle in a circle is formed by two rays (sides of the angle) that share a common endpoint (the vertex) and are drawn from the center of the circle to the circumference.

Front

What is the measure of a central angle?

Back

A central angle is equal to the measure of the arc it intercepts.

Front

What is an inscribed angle?

Back

An inscribed angle is formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle, and the sides of the angle are determined by the chords.

Front

How do you calculate the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

What is the relationship between angles formed by intersecting chords?

Back

The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Front

What is the relationship between angles formed by a tangent and a chord?

Back

The measure of the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the intercepted arc.

Front

What is the measure of the angle formed by two tangents drawn from a point outside the circle?

Back

The measure of the angle formed by two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the formula for the sum of the interior angles of a polygon?

Back

The sum of the interior angles of a polygon with n sides is (n-2) × 180 degrees.

Front

What is the definition of a semicircle?

Back

A semicircle is an arc that represents half of a circle, and the angle formed at the endpoints of the arc is a right angle (90 degrees).

Front

What is the relationship between the angles in a cyclic quadrilateral?

Back

In a cyclic quadrilateral, the sum of the opposite angles is equal to 180 degrees.