Understanding Circles and Angles

The video tutorial covers various aspects of circle geometry, focusing on central angles, inscribed angles, and quadrilaterals inscribed in circles. It explains the congruence between central angles and their intercepted arcs, the properties of inscribed angles, and how to calculate angles that are neither central nor inscribed by using intercepted arcs. The tutorial also discusses the supplementary nature of opposite angles in quadrilaterals inscribed in circles.

What is the measure of a central angle if the intercepted arc is 135 degrees?

• 90 degrees

• 45 degrees

• 135 degrees

• 180 degrees

Which of the following is true about central angles and their intercepted arcs?

• Central angles are twice the intercepted arc

• Central angles and intercepted arcs are congruent

• Central angles are half the intercepted arc

• Central angles are always larger

If a central angle measures 96 degrees, what is the measure of the intercepted arc?

• 192 degrees

• 144 degrees

• 48 degrees

• 96 degrees

An inscribed angle is half the measure of its intercepted arc. If the arc is 70 degrees, what is the inscribed angle?

• 70 degrees

• 35 degrees

• 140 degrees

• 105 degrees

What is the measure of an inscribed angle if the intercepted arc is 140 degrees?

• 70 degrees

• 140 degrees

• 210 degrees

• 35 degrees

What is the relationship between opposite angles in a quadrilateral inscribed in a circle?

• They are equal

• They are congruent

• They are complementary

• They are supplementary

If one angle of an inscribed quadrilateral is 80 degrees, what is the measure of its opposite angle?

• 180 degrees

• 100 degrees

• 90 degrees

• 80 degrees

How do you find the measure of an angle inside a circle that is not at the center or inscribed?

• Double the intercepted arc

• Add the intercepted arcs and divide by two

• Multiply the intercepted arcs

• Subtract the intercepted arcs

If the intercepted arcs are 160 and 50 degrees, what is the measure of the angle inside the circle?

• 105 degrees

• 55 degrees

• 80 degrees

• 210 degrees

What is the measure of a vertical angle if the angle inside the circle is 105 degrees?

• 105 degrees

• 90 degrees

• 210 degrees

• 52.5 degrees