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 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.) 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.)

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has 360 degrees.

Step2: Calculate the angle for each known percentage

For Division A: Since it is 27% of the total sales, the angle is $0.27\times360 = 97.2$.
For Division B: As it is 23% of the total sales, the angle is $0.23\times360=82.8$.
For Division D: Given it is 18% of the total sales, the angle is $0.18\times360 = 64.8$.
For Division F: Since it is 13% of the total sales, the angle is $0.13\times360=46.8$.
For Division C: We know the angle is 32.4. To find the percentage, we use the formula $\text{Percentage}=\frac{\text{Angle}}{360}\times100$. So, $\frac{32.4}{360}\times100 = 9$.
For Division E: We know the angle is 36. Using the formula $\text{Percentage}=\frac{\text{Angle}}{360}\times100$, we get $\frac{36}{360}\times100 = 10$.
To find the percentage for a division, divide the measure of the angle formed by its segment by 360 and multiply the result by 100.

Answer:

To find the percentage for a division, divide the measure of the angle formed by its segment by 360 and multiply the result by 100.