Understanding Inscribed Quadrilaterals

The video tutorial explains Theorem 10.10, which states that a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. It details how inscribed angles relate to intercepted arcs, showing that the sum of opposite angles equals 180°. The tutorial includes example problems to find unknown variables in inscribed quadrilaterals, reinforcing the concept of supplementary angles. The video concludes with a review of key points, emphasizing the relationship between inscribed angles and their intercepted arcs.

What does Theorem 10.10 state about inscribed quadrilaterals?

• Their adjacent angles are supplementary.

• Their opposite angles are supplementary.

• Their adjacent angles are equal.

• Their opposite angles are equal.

Why are the opposite angles of an inscribed quadrilateral supplementary?

• Because they are equal to each other.

• Because they intercept the same arc.

• Because they are half the measure of their intercepted arcs.

• Because they form a straight line.

In an inscribed quadrilateral, if angle A is 70°, what is the measure of angle C?

• 90°

• 110°

• 70°

• 180°

If angle B is 80° in an inscribed quadrilateral, what is the measure of angle D?

• 80°

• 90°

• 180°

• 100°

In the example problem, what is the value of y if angle E is opposite angle C and angle C is 75°?

• 90°

• 75°

• 105°

• 180°

In the second example, if angle C is 62°, what is the measure of angle E?

• 180°

• 90°

• 118°

• 62°

What is the value of x if angle B is 10x and angle D is 8x in the second example?

• 5

• 10

• 15

• 20

What is the relationship between an inscribed angle and its intercepted arc?

• The inscribed angle is equal to the intercepted arc.

• The inscribed angle is twice the intercepted arc.

• The inscribed angle is unrelated to the intercepted arc.

• The inscribed angle is half the intercepted arc.

What condition must be met for a triangle to be a right triangle in a circle?

• Its hypotenuse must be the diameter.

• Its adjacent angles must be equal.

• Its opposite angles must be supplementary.

• Its sides must be equal.

What happens if two angles intercept the same arc in a circle?

• They are unrelated.

• They are equal to the arc.

• They are congruent.

• They are supplementary.