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. division b 23% division c division d 18% division a 27% 13% division f division e a 97.2 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 32.4. this corresponds to 9%. (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 e is 36. this corresponds to 10%. (type integers or decimals. do not include the degree symbol in your answers.) to find the percentage for a division, divide the measure of the angle formed by its segment by and the result by (type integers or decimals. do not include the degree symbol in your answers.) video textbook get more help -

Explanation:

Step1: Recall total degrees in a circle

A full - circle has 360 degrees.

Step2: Calculate angle for Division A

Since Division A is 27% of the sales, the angle is $0.27\times360 = 97.2$.

Step3: Calculate angle for Division B

As Division B is 23% of the sales, the angle is $0.23\times360=82.8$.

Step4: Calculate angle for Division D

Given Division D is 18% of the sales, the angle is $0.18\times360 = 64.8$.

Step5: Calculate angle for Division F

Since Division F is 13% of the sales, the angle is $0.13\times360=46.8$.

Step6: Calculate percentage for Division C

The angle for Division C is 32.4. The percentage is $\frac{32.4}{360}\times100 = 9$.

Step7: Calculate percentage for Division E

The angle for Division E is 36. The percentage is $\frac{36}{360}\times100 = 10$.

Answer:

Angles: Division A: 97.2, Division B: 82.8, Division D: 64.8, Division F: 46.8, Division C: 32.4, Division E: 36.
Percentages: Division A: 27%, Division B: 23%, Division D: 18%, Division F: 13%, Division C: 9%, Division E: 10%