Inscribed Angles and Quadrilaterals in Circles

Front

What is an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle.

Front

What is the relationship between an inscribed angle and the arc it intercepts?

Back

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

Front

If an inscribed angle intercepts an arc of 80 degrees, what is the measure of the inscribed angle?

Back

40 degrees.

Front

What is a cyclic quadrilateral?

Back

A cyclic quadrilateral is a four-sided figure (quadrilateral) where all vertices lie on the circumference of a circle.

Front

What is the property of opposite angles in a cyclic quadrilateral?

Back

The sum of the opposite angles in a cyclic quadrilateral is 180 degrees.

Front

If angle A and angle C are opposite angles in a cyclic quadrilateral, and angle A measures 70 degrees, what is the measure of angle C?

Back

110 degrees.

Front

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

Back

The sum of the interior angles of a quadrilateral is 360 degrees.

Front

What is the measure of an angle at the center of a circle compared to an inscribed angle that subtends the same arc?

Back

The angle at the center is twice the measure of the inscribed angle.

Front

If an inscribed angle measures 30 degrees, what is the measure of the arc it intercepts?

Back

60 degrees.

Front

What is the definition of a chord in a circle?

Back

A chord is a line segment with both endpoints on the circle.