#1
In a circle with center O, if angle AOB is 60 degrees, what is the measure of the arc AB?
120 degrees
ExplanationThe measure of an arc is twice the measure of its corresponding central angle.
#2
If a central angle of a circle measures 45 degrees, what is the measure of the corresponding arc?
45 degrees
ExplanationThe measure of the central angle and its corresponding arc are equal in a circle.
#3
In a cyclic quadrilateral, what is the sum of opposite angles?
180 degrees
ExplanationOpposite angles in a cyclic quadrilateral add up to 180 degrees.
#4
If an inscribed angle in a circle measures 30 degrees, what is the measure of the intercepted arc?
60 degrees
ExplanationThe measure of the intercepted arc is twice the measure of the inscribed angle.
#5
If the measure of an inscribed angle is 90 degrees, what is the measure of the intercepted arc?
180 degrees
ExplanationAn inscribed angle of 90 degrees corresponds to an intercepted arc of 180 degrees.
#6
In a circle with radius 5 units, what is the length of the arc formed by a central angle of 72 degrees?
6π units
ExplanationThe length of an arc is given by the formula: arc length = radius × central angle (in radians).
#7
For a cyclic quadrilateral, if one angle is 80 degrees, what is the measure of the opposite angle?
100 degrees
ExplanationOpposite angles in a cyclic quadrilateral add up to 180 degrees.
#8
For a regular hexagon inscribed in a circle, what is the measure of each central angle?
60 degrees
ExplanationIn a regular hexagon inscribed in a circle, each central angle measures 60 degrees.
#9
If an inscribed angle in a circle measures 120 degrees, what is the measure of the central angle subtended by the same arc?
240 degrees
ExplanationThe central angle subtended by an inscribed angle is twice the measure of the inscribed angle.
#10
For a circle with radius 8 units, what is the length of the arc subtended by a central angle of 45 degrees?
4π units
ExplanationArc length = radius × central angle (in radians); here, central angle is given in degrees.
#11
If the measure of an inscribed angle is 60 degrees, what is the measure of the central angle subtended by the same arc?
180 degrees
ExplanationThe central angle subtended by an inscribed angle is twice the measure of the inscribed angle.
#12
In a circle with radius 10 units, if the central angle is 120 degrees, what is the length of the intercepted arc?
20π units
ExplanationArc length = radius × central angle (in radians); here, central angle is given in degrees.