Inscribed angle And Cyclic Quadrilateral

Front

What is an inscribed angle in a circle?

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 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 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 opposite angles in a cyclic quadrilateral are supplementary, meaning they add up to 180°.

Front

If an arc measures 100°, what is the measure of the inscribed angle that intercepts it?

Back

50°

Front

In a cyclic quadrilateral, if three angles are 70°, 80°, and 30°, what is the measure of the fourth angle?

Back

The fourth angle is 100°.

Front

What is the relationship between the inscribed angle and the central angle that intercepts the same arc?

Back

The inscribed angle is half the measure of the central angle that intercepts the same arc.

Front

If an inscribed angle measures 45°, what is the measure of the intercepted arc?

Back

90°

Front

What is the sum of the angles in a cyclic quadrilateral?

Back

The sum of the angles in a cyclic quadrilateral is 360°.

Front

If one angle of a cyclic quadrilateral is 120°, what is the measure of its opposite angle?

Back

The opposite angle is 60°.