Circle Arcs & Angles Quiz

What is the measure of arc KL?

• 108

• 106

• 110

• 112

Answer explanation

The measure of arc KL is 108 degrees because it is the correct choice among the given options.

What is the measure of a central angle that subtends an arc of 100 degrees in a circle?

• 50 degrees

• 100 degrees

• 150 degrees

• 200 degrees

Answer explanation

The measure of a central angle is equal to the measure of the arc it subtends, so a central angle that subtends an arc of 100 degrees in a circle is 100 degrees.

If a central angle measures 80 degrees, what is the measure of the arc it subtends?

• 40 degrees

• 80 degrees

• 160 degrees

• 320 degrees

Answer explanation

The measure of the arc is equal to the measure of the central angle, so the arc subtends 80 degrees.

In a circle, if the arc length between two points is 120 degrees, what is the measure of the central angle?

• 60 degrees

• 120 degrees

• 180 degrees

• 240 degrees

Answer explanation

The measure of the central angle in a circle is equal to the arc length between two points, which is 120 degrees in this case, so the central angle is also 120 degrees.

What is the relationship between the central angle and the arc it subtends?

• The central angle is half the measure of the arc.

• The central angle is twice the measure of the arc.

• The central angle has the same measure as the arc.

• There is no specific relationship.

Answer explanation

The central angle has the same measure as the arc.

A circle has a central angle of 45 degrees. What is the measure of the arc subtended by this angle?

• 22.5 degrees

• 45 degrees

• 90 degrees

• 180 degrees

Answer explanation

The measure of the arc subtended by a central angle is equal to the measure of the central angle itself. Therefore, the arc subtended by a 45-degree central angle is also 45 degrees.

If two arcs in a circle are congruent, what can be said about their corresponding central angles?

• They are supplementary.

• They are congruent.

• They are complementary.

• They are not necessarily equal.

Answer explanation

The central angles of congruent arcs in a circle are also congruent.

An inscribed angle in a circle subtends an arc of 100 degrees. What is the measure of the inscribed angle?

• 50 degrees

• 100 degrees

• 150 degrees

• 200 degrees

Answer explanation

The measure of an inscribed angle is half the measure of the arc it subtends. Therefore, the inscribed angle measures 50 degrees (100 degrees / 2 = 50 degrees).

In a circle, if an inscribed angle measures 30 degrees, what is the measure of the arc it subtends?

• 30 degrees

• 60 degrees

• 120 degrees

• 180 degrees

Answer explanation

The measure of the arc subtended by an inscribed angle is twice the measure of the angle itself. Therefore, the arc measures 60 degrees (2 * 30 degrees).

A circle has an inscribed angle that intercepts an arc measuring 150 degrees. What is the measure of the inscribed angle?

• 75 degrees

• 150 degrees

• 225 degrees

• 300 degrees

Answer explanation

The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, the inscribed angle measures 75 degrees (150 degrees / 2 = 75 degrees).