Proving Opposite Angles in Inscribed Quadrilaterals

The video tutorial explains the proof that opposite angles of an inscribed quadrilateral are supplementary. It begins by setting up the problem and defining the terms. The proof involves understanding the relationship between inscribed angles and the arcs they intercept. By calculating the measures of these arcs and their corresponding angles, the video demonstrates that the sum of opposite angles equals 180 degrees, thus proving they are supplementary.

What does it mean for angles to be supplementary?

• They are adjacent to each other

• They are always equal

• Their measures add up to 180 degrees

• Their measures add up to 90 degrees

What geometric shape is being discussed in terms of inscribed angles and supplementary properties?

• Circle

• Pentagon

• Quadrilateral

• Triangle

What is the initial assumption made about one of the angles in the quadrilateral?

• It is an obtuse angle

• It measures 90 degrees

• It measures 180 degrees

• It measures x degrees

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

• The arc is triple the angle

• The angle is equal to the arc

• The arc is double the angle

• The angle is double the arc

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

• 360 degrees

• x degrees

• 2x degrees

• 180 degrees

What does the measure of an inscribed angle depend on?

• The diameter of the circle

• The radius of the circle

• The circumference of the circle

• The arc it intercepts

What is the measure of the arc that completes the circle if one arc measures 2x degrees?

• 360 degrees

• 180 degrees

• 2x degrees

• 360 minus 2x degrees

What is the measure of the angle that intercepts the arc measuring 360 minus 2x degrees?

• x degrees

• 180 degrees

• 360 degrees

• 180 minus x degrees

How do you prove that opposite angles in an inscribed quadrilateral are supplementary?

• By proving the sum of opposite angles is 180 degrees

• By proving each angle is less than 180 degrees

• By proving the sum of angles is 360 degrees

• By proving each angle is 90 degrees

What is the result when you add the measures of the two opposite angles discussed?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees