a If the whole circle has an arc measure of 360, then the arc that represents p % of the circle has a measure of p %*360.
B
b Notice that a major arc has a measure greater than 180, which corresponds to at least 50 % of the circle.
C
c Congruent arcs represent the same part of a circle.
A
aMall: 273.6
Vintage Stores: 14.4
B
bMall: A major arc
None of These: A minor arc
C
c Yes, see solution.
Practice makes perfect
a Looking at the graph, we can see that the arc that represents the Mall is 76 % of the whole. Therefore, to find the measure of this arc we need to evaluate 76 % of 360.
The arc that represents this category has a measure of 273.6 degrees. Next we will find the measure of arc that represents the Vintage Stores. To do this we will evaluate 4 % of 360.
The arc that represents Vintage Stores has a measure of 14.4 degrees.
b Let's begin with recalling that a major arc has a measure greater than 180, which corresponds to at least 50 % of the circle. Additionally, any arc that represents less than 50 % of the circle is a minor arc. Now we can describe the kind of arc associated with the given categories.
Category
Part of Circle
Greater than 50 %?
Type of Arc
Mall
76 %
Yes
Major arc
None of these
9 %
No
Minor arc
c To determine if there are any congruent arcs in the graph, remember that congruent arcs represent the same part of a circle. Therefore, since both None of these and the Online categories represent 9 % of the circle, the arcs that represent these categories are congruent.
