Angle Measurements: Circle Graph

by Jamey
(USA)

Question
A class budget consists of $900 for dances, $1200 for trips, and $600 for charity. If the data were presented in a circle graph, what will be the angle measure of the part labeled "dances"?

Answer
STEP 1:    Let us first organize the given data into a table.
activity-budget table

A circle graph is usually a circular chart which is divided into sectors illustrating percents. Since you are given three items, the circle will have three pie pieces.

STEP 2:    To create the circle graph, the first step you will need to do is to make each of the numbers into a fraction out of the total. The total budget is 600 + 900 + 1200, or $2700.

The part representing "dances” will then be 900/2700 of 1/3.

Similarly, the parts representing “charity” and “trip” will be 2/9 and 4/9 respectively.

Here’s how the circle graph looks like:

trips-dances-charity pie chart
The arc length of each sector is equal to the quantity it represents.

STEP 3:   Now, we know that a circle measures in total. If you
multiply the fraction representing a part of the circle by 360°, then you get the angle measure of that part.

You need to find the angle measure of the part labeled "dances". For this multiply 1/3 by 360°.

1/3 multiply by 360 gives 120 degree

The angle measure of the part labeled "dances" is obtained as 120°.

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