Exploring Inscribed Angles in Geometry

What defines an inscribed angle in a circle?

• An angle with its vertex at the center of the circle

• An angle created by two radii of the circle

• An angle with its vertex on the circle and sides intersecting the circle

• An angle outside the circle intercepting two tangents

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

• One-fourth the arc's measure

• Half the arc's measure

• Twice the arc's measure

• Equal to the arc's measure

What is true about two inscribed angles that intercept the same arc?

• They are supplementary

• They are complementary

• They are congruent

• They are adjacent

What is the measure of an angle inscribed in a semicircle?

• 90 degrees

• 180 degrees

• 360 degrees

• 45 degrees

How do the opposite angles of a quadrilateral inscribed in a circle relate to each other?

• They are congruent

• They are identical

• They are supplementary

• They are complementary

If an inscribed angle measures 60 degrees, what is the measure of its intercepted arc?

• 60 degrees

• 30 degrees

• 180 degrees

• 120 degrees

If an angle intercepts a semicircle, what type of angle is it?

• Straight angle

• Obtuse angle

• Right angle

• Acute angle

What is the measure of an angle formed by a tangent and a chord at the point of tangency?

• Equal to the intercepted arc's measure

• One-fourth the intercepted arc's measure

• Twice the intercepted arc's measure

• Half the intercepted arc's measure

If the measure of arc PMQ is 212 degrees, what is the measure of angle PQR?

• 106 degrees

• 74 degrees

• 212 degrees

• 148 degrees

What is the relationship between the measure of an angle created by a chord and a tangent and its intercepted arc?

• It is one-fourth the arc's measure

• It is half the arc's measure

• It is double the arc's measure

• It is equal to the arc's measure