A polygon is chosen at random from five regular polygons with 3, 4, 5, 6, and 8 sides. What is the probability that the measure of each angle of the polygon is a multiple of 30°?
the angles are for eavh n,
3 60
4 90
5 108
6 120
8 135
so your chance is 3/5
To find the probability that the measure of each angle of the randomly chosen polygon is a multiple of 30°, we need to determine the favorable outcomes and the total possible outcomes.
Favorable outcomes:
A regular polygon with all interior angles being a multiple of 30° will have angles measuring 30°, 60°, 90°, 120°, 150°, 180°, etc.
The regular polygons with 3 and 4 sides don't have interior angles that are multiples of 30°. So, we can exclude them from the favorable outcomes.
The remaining regular polygons with 5, 6, and 8 sides have angles measuring 60°, 120°, and 150°, which are all multiples of 30°.
Therefore, out of the five regular polygons, three of them have angles that are multiples of 30°.
Total possible outcomes:
There are five regular polygons to choose from.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
= 3 / 5
= 0.6
Therefore, the probability that the measure of each angle of the randomly chosen polygon is a multiple of 30° is 0.6 or 60%.
To find the probability that the measure of each angle of the polygon is a multiple of 30°, we need to determine the favorable outcomes (i.e., the number of regular polygons out of the five) and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. A polygon with each angle having a multiple of 30° must have an interior angle of 60°, 90°, 120°, 150°, or 180°.
Out of the given five regular polygons, only the polygons with 3 and 6 sides fulfill this requirement. Both an equilateral triangle and a regular hexagon have angles measuring multiples of 30° (60° and 120°, respectively), while the other polygons such as squares, pentagons, and octagons do not.
Thus, the number of favorable outcomes is 2.
Now, let's determine the total number of possible outcomes. Since we are choosing a polygon at random from the five given options, the total number of possible outcomes is simply 5.
Finally, we can calculate the probability. The probability of an event occurring is given by:
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, the probability is:
Probability = 2 / 5
Hence, the probability that the measure of each angle of the polygon is a multiple of 30° is 2/5 or 0.4 (40%).