Question

A central angle is best described as which of the following?
a. it is part of the circumference of a circle
b. it is an angle that has its vertex on the circle
c. it is an angle that has its vertex at the center of the circle
d. it has a measure greater than 180 degrees

Answer 1

Answer:It is the angle having a measure more than 180°

Answer 2

A central angle is best described as in option c - "it is an angle that has its vertex at the centre of the circle".

• We know that the angle between two 'radii' of a circle is called a 'central angle'.
• The value of a 'central angle' can differ from 0° to 360°
• Option a states that the 'central angle' is a part of the 'circumference' of a circle. But a 'central angle' is measured from the 'centre' of a circle. So option a is incorrect.
• Option b states that the 'central angle' has its 'vertex' on the circle. But the vertex of a 'central angle' is at the 'centre' of the circle. So option b is incorrect.
• Option c states that the vertex of a 'central angle' is at the 'centre' of the circle. So option c is correct.
• Option d states that the measure of a 'central angle' can be greater than 180°. Though the statement about the 'central angle' is true, this statement does not describe the 'central angle' well enough. So option d is also incorrect.

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