Question

the graph shows percentages of sales made by various divisions of a company in one year. what are the angles formed by the segments for each division? what are the missing percentages? explain how you were able to determine each percentage. find the angles formed by the segments for each division for which a percentage is given.

division	measure of angle formed by segment for division
b	82.8
d	64.8
f	46.8

(type integers or decimals. do not include the degree symbol in your answers.) by the vertical angles theorem and the angle addition postulate, the measure of the angle formed by the segment for division c is . this corresponds to %. (type integers or decimals. do not include the degree symbol in your answers.)

Explanation:

Step1: Recall the relationship between percentage and angle in a pie - chart

The total angle in a circle is 360 degrees. To find the angle of a segment, we use the formula $\text{Angle}=\text{Percentage}\times360$. To find the percentage from the angle, we use the formula $\text{Percentage}=\frac{\text{Angle}}{360}\times100$.

Step2: Calculate the angle for known percentages

For Division A: Given percentage = 27%, Angle = $0.27\times360 = 97.2$.
For Division B: Given percentage = 23%, Angle = $0.23\times360=82.8$.
For Division D: Given percentage = 18%, Angle = $0.18\times360 = 64.8$.
For Division F: Given percentage = 13%, Angle = $0.13\times360=46.8$.

Step3: Calculate the missing percentage for Division C

The sum of the known percentages is $27 + 23+18 + 13=81\%$. So the percentage for Division C is $100 - 81=19\%$.

Step4: Calculate the angle for Division C

Using the formula $\text{Angle}=\text{Percentage}\times360$, for Division C with percentage 19%, Angle = $0.19\times360 = 68.4$.

Answer:

Division	Measure of Angle Formed by Segment for Division
B	82.8
C	68.4
D	64.8
F	46.8

The percentage for Division C is 19.