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Five points on a circle separate the circle into five congruent arcs.
a. What is the degree measure of each arc? .
b. If the radius of the circle is 3 cm, what is the length of each arc?
c. Suppose the points are connected consecutively with line segments. How do you describe the figure formed?

Sagot :

a circle divided into five equal parts:

1 part = 1/5

a.)  A circle has a full 360 degrees.
     1/5 (360 degrees) = 72 degrees
      Each arc has a measure of 72 degrees.
      The central angle = degree measure of intercepted arc

b.)  Step 1:  Find the circumference (C), when radius = 3 cm;  π=3.14  (pi)
     C = 2π r
     C = 2 (3.14) (3 cm)
        =  (6.28) (3 cm)
        = 18.84 cm
   Step 2:  Find the length (in cm) of each arc.
       Arc length =     central angle    ×  Circumference
                              360 dgrees
       Arc length =    72 degrees   x   18.84 cm
                             360 degrees
       Arc length = (1/5) ( 18.84 cm)
       Arc length = 3.768 cm or 3. 77 cm rounded off to the nearest hundredths
          Each arc has a length of 3.77 cm.

c.)  Pentagon, a polygon with five sides, is formed.


      

                  




Assoneidn
a. each arc measures 72 
b. 3.78 cm is the length of each arc
c. a regular polygon having 5 equal sides called PENTAGON. :)
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