emma draws this diagram. She says it shows part of a regular polygon. Explain how you can tell that Emma must have made a mistake (it is a 158 degree angle)
For a regular polygon, external angles at each corner must be evenly divisible into 360. 158 degrees does not satisfy that requirement As for internal angles,A, they must satisfy
A = 180 - 360/N, where N is the number of sides. 158 degrees does not satisdfy that reurment either
Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 80 people.
(a) How many would you expect to be between 157 and 173 cm tall?
(b) How many would you expect to be taller than 160 cm?
To determine if Emma made a mistake, we can use the following reasoning:
In a regular polygon, all angles have equal measures. If Emma claims that the angle in the diagram is 158 degrees and it is part of a regular polygon, we can calculate the measure of each angle in the polygon by dividing the total sum of angles in the polygon by the number of sides.
The formula to find the sum of the interior angles of a polygon is given by:
Sum = (n - 2) * 180 degrees,
where "n" represents the number of sides of the polygon.
Let's calculate the measure of each angle in a regular polygon using the number of sides corresponding to a 158-degree angle.
1. Take the measure of each angle in the regular polygon: (n - 2) * 180 degrees.
For example, a triangle (n = 3) has angles measuring (3 - 2) * 180 degrees = 180 degrees.
A square (n = 4) has angles measuring (4 - 2) * 180 degrees = 360 degrees.
A pentagon (n = 5) has angles measuring (5 - 2) * 180 degrees = 540 degrees.
2. Now, divide the calculated sum by the number of sides to find the measure of each angle.
For a triangle, 180 degrees ÷ 3 = 60 degrees.
For a square, 360 degrees ÷ 4 = 90 degrees.
For a pentagon, 540 degrees ÷ 5 = 108 degrees.
Since the angle in Emma's diagram measures 158 degrees, it cannot be part of a regular polygon with any whole number of sides. Regular polygons always have angles with equal measures, and Emma's angle of 158 degrees does not match the calculated measures for any regular polygon.
Therefore, based on this reasoning, we can conclude that Emma made a mistake in claiming that her diagram shows part of a regular polygon.