Inscribed Angles and Arc Measures

The video tutorial explains the concept of inscribed angles in geometry, highlighting that the measure of an inscribed angle is half the measure of its intercepted arc. It demonstrates how to construct equations using these properties and solve for unknown variables. The tutorial emphasizes understanding the relationship between inscribed angles and arc measurements, using examples to illustrate these concepts.

What is an inscribed angle?

• An angle formed by two radii of a circle.

• An angle with its vertex on the circle and sides containing chords of the circle.

• An angle formed by two tangents to a circle.

• An angle formed by a tangent and a chord.

How is the measure of an inscribed angle related to its intercepted arc?

• It is twice the arc measure.

• It is unrelated to the arc measure.

• It is equal to the arc measure.

• It is half the arc measure.

If an inscribed angle measures 33°, what is the measure of its intercepted arc?

• 99°

• 132°

• 33°

• 66°

What is the measure of a semicircle?

• 90°

• 360°

• 180°

• 270°

When constructing equations with inscribed angles, what is a key consideration?

• The angles are twice the measure of their arcs.

• The angles are half the measure of their arcs.

• The sum of the angles is always 360°.

• The angles are always equal.

How do inscribed angles differ from central angles?

• Inscribed angles are always larger.

• Inscribed angles are half the measure of their arcs.

• Central angles are half the measure of their arcs.

• Central angles are unrelated to arcs.

What is the sum of the measures of two inscribed angles that intercept the same arc?

• Half the arc measure.

• Twice the arc measure.

• Equal to the arc measure.

• Unrelated to the arc measure.

If the equation 5x - 2 + 2x + 8 = 90 is given, what is the value of x?

• 10

• 12

• 14

• 16

What is the measure of an arc if the inscribed angle is 45°?

• 180°

• 90°

• 45°

• 135°

If two inscribed angles intercept the same arc, what can be said about their measures?

• One is half the other.

• They are unrelated.

• One is double the other.

• They are equal.