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

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

Back

The measure of an inscribed angle is half the measure of the arc it intercepts.

Front

Define 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 60°, what is the measure of the inscribed angle that intercepts it?

Back

30° (because the inscribed angle is half the arc measure).

Front

Calculate the fourth angle of a cyclic quadrilateral if three angles measure 70°, 80°, and 50°.

Back

The fourth angle measures 20° (since 70° + 80° + 50° + x = 360°, x = 360° - 200°).

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 angle A measures 45° and angle B is its opposite angle in a cyclic quadrilateral, what is the measure of angle B?

Back

135° (since opposite angles are supplementary: 180° - 45° = 135°).

Front

True or False: The inscribed angle theorem states that an inscribed angle is equal to the arc it intercepts.

Back

False (the inscribed angle is half the measure of the intercepted arc).

Front

What is the measure of an inscribed angle that intercepts an arc measuring 100°?

Back

50° (because the inscribed angle is half the arc measure).