Geometry-Angles in a Circle

If arc XV = 70° and ∠YUV = 43°, how do you find the measure of arc YX?

• 27°

• 43°

• 70°

• 50°

If arc AB measures 70° and angle AOB is formed at the center, what is the measure of angle AOB?

• 50°

• 70°

• 90°

• 60°

What is the relationship between the measure of an arc and the angle subtended by it at the center of the circle?

• The measure of the angle at the center is equal to the measure of the arc.

• The measure of the angle at the center is half the measure of the arc.

• The measure of the angle at the center is twice the measure of the arc.

• The measure of the angle at the center is unrelated to the measure of the arc.

How do you calculate the measure of an angle formed by two intersecting chords inside a circle?

• The measure of the angle is equal to the difference of the measures of the intercepted arcs.

• The measure of the angle is half the sum of the measures of the intercepted arcs.

• The measure of the angle is equal to the sum of the measures of the intercepted arcs.

• The measure of the angle is equal to the average of the measures of the intercepted arcs.

How do you find the measure of an angle formed by two chords intersecting inside a circle?

• The measure of the angle is half the sum of the measures of the arcs intercepted by the angle.

• The measure of the angle is equal to the difference of the measures of the arcs intercepted by the angle.

• The measure of the angle is equal to the sum of the measures of the arcs intercepted by the angle.

• The measure of the angle is equal to the measure of the larger arc intercepted by the angle.

What is the measure of an angle formed by a tangent and a chord through the point of contact?

• The measure of the angle is equal to the measure of the opposite arc.

• The measure of the angle is half the sum of the measures of the intercepted arcs.

• The measure of the angle is equal to the sum of the measures of the intercepted arcs.

• The measure of the angle is equal to the measure of the tangent line.

If two angles are formed by intersecting chords, how do you find their measures?

• Each angle is half the sum of the measures of the arcs intercepted by the angle.

• Each angle is equal to the difference of the measures of the arcs intercepted by the angle.

• Each angle is the average of the measures of the two angles formed by the intersecting chords.

• Each angle is equal to the sum of the measures of the arcs intercepted by the angle.

What is the significance of the diameter in a circle regarding angles?

• An angle inscribed in a semicircle is a right angle (90°).

• The diameter is the longest chord in a circle.

• The diameter divides the circle into two equal halves.

• The diameter has no effect on the angles in a circle.

What is the measure of an angle formed by two secants intersecting outside a circle?

• The measure of the angle is half the sum of the measures of the intercepted arcs.

• The measure of the angle is equal to the measure of the larger intercepted arc.

• The measure of the angle is half the difference of the measures of the intercepted arcs.

• The measure of the angle is equal to the measure of the smaller intercepted arc.

If m∠A = 95° in a cyclic quadrilateral ABCD, what can be concluded about m∠C?

• m∠C = 85° (because m∠A + m∠C = 180°)

• m∠C = 95° (because opposite angles are equal)

• m∠C = 75° (because m∠A is greater than 90°)

• m∠C = 65° (because m∠A is less than 100°)