Inscribed angle And Cyclic Quadrilateral Period 5 & 8

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 a cyclic quadrilateral has three angles measuring 110°, 40°, and 90°, what is the measure of the fourth angle?

Back

120°

Front

What is the inscribed angle theorem?

Back

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

Front

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

Back

40°

Front

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

Back

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

Front

How do you calculate the fourth angle of a cyclic quadrilateral?

Back

To find the fourth angle, subtract the sum of the three known angles from 360°.

Front

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

Back

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

Front

If angle A measures 79° in a cyclic quadrilateral, what is the measure of its opposite angle?

Back

101° (since opposite angles are supplementary, 180° - 79° = 101°).

Front

What is the measure of angle B if angle A is 93° and they are opposite angles in a cyclic quadrilateral?

Back

87° (since opposite angles are supplementary, 180° - 93° = 87°).