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What type of arc lies between the two sides of a central angle and measures less than 180 degrees?
Minor arc
What is defined to be an arc that lies between the sides of an obtuse inscribed angle?
There are three possibilities for the arc that lies between the sides of an angle (at the centre of the circle):semi-circleminor arcmajor arcWith any two points of the circumference of a circle they will make an angle at the centre of the circle.If the angle is 180o, then the two points lie on either end of a diameter and both arcs are the same length and are a semi-circle.Otherwise, the minor arc is the shorter of the two arcs, the major one is the longer one:The minor arc is the side of the angle that is smaller, ie the angle is acute (< 90o), a right angle (= 90o) or obtuse (> 90o & < 180o).The major arc is the side of the angle that is bigger, ie the angle is reflex (> 180o).
What is the relation between area of a sector and length of an arc of a circle?
There is no direct relation between the area of a sector and the length of an arc. You must know the radius (or diameter) or the angle of the sector at the centre.
What angle has the same measure as its arc?
Central angle
How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
