Exploring Central and Inscribed Angles

What defines a central angle in a circle?

• An angle formed outside the circle

• An angle with its vertex on the circle's circumference

• An angle with its sides tangent to the circle

• An angle with its vertex at the center of the circle and its sides as radii

What is the relationship between the measure of a central angle and its intercepted arc?

• The angle's measure is half of the arc's measure

• The angle's measure is twice the arc's measure

• The angle's measure is equal to the arc's measure

• There is no relationship

If two central angles are congruent, what can be said about the chords they intercept?

• The chords are perpendicular

• The chords are parallel

• The chords are congruent

• The chords have no specific relationship

How can congruent chords in a circle affect central angles?

• There is no effect

• Make them supplementary

• Make them perpendicular

• Make them congruent

What theorem is applied when two triangles in a circle are congruent by side-angle-side?

• Pythagorean theorem

• Chord congruence theorem

• Triangle congruence theorem

• Central angle theorem

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

• Equal to the arc's measure

• One-fourth the arc's measure

• Twice the arc's measure

• Half the arc's measure

An angle inscribed in a semicircle forms what type of angle?

• Acute angle

• Straight angle

• Obtuse angle

• Right angle

If two inscribed angles intercept the same arc, what can be inferred about these angles?

• They are congruent

• They are adjacent

• They are complementary

• They are supplementary

In a circle, if an inscribed angle measures 40 degrees, what is the measure of its intercepted arc?

• 40 degrees

• 80 degrees

• 160 degrees

• 120 degrees

Given a circle with a triangle inscribed in it, if the arcs are in the ratio 2:3:7, what is the measure of the smallest arc?

• 30 degrees

• 60 degrees

• 90 degrees

• 210 degrees