Question

What is the set of angle sizes that are multiples of 45 degrees and less than 27 degrees?

a. {0, 45, 90}
b. {0, 45, 90, 135, 180}
c. {0, 45, 90, 135, 180, 225}
d. {0, 45, 90, 135, 180, 225, 270}

Answer 1

The set of angle sizes that is a multiple of 45 degrees and less than 27 degrees contains only the angle of 0 degrees. None of the provided options (a, b, c, d) are correct as they list angles greater than 27 degrees except for 0 degrees.

Step-by-step explanation:

Identifying Multiples of 45 Degrees Less Than 27 Degrees

The question asks what is the set of angle sizes that are multiples of 45 degrees and less than 27 degrees. To find this, we must list out the multiples of 45 degrees and then identify which of those are less than 27 degrees. The multiples of 45 degrees are 0, 45, 90, 135, 180, and so on. However, because we are looking for angles that are less than 27 degrees, none of the multiples other than 0 degrees will apply since all other multiples of 45 degrees are greater than 27 degrees. Therefore, the set of angle sizes that match the criteria is simply {0}.

Options a, b, c, and d provided in the question all list angles that exceed 27 degrees, other than the 0 degrees. So none of these options are correct.

Answer 2

The only multiple of 45 degrees that is less than 27 degrees is 0 degrees. Therefore, the set of angle sizes that fulfill the condition is {0}.

Step-by-step explanation:

The question requires identifying the set of angle sizes that are multiples of 45 degrees, but which are also less than 27 degrees. To solve this, we must look at multiples of 45 degrees: 0, 45, 90, 135, 180, 225, and 270 degrees. However, since we are only looking for angles less than 27 degrees, the only multiple of 45 degrees less than 27 degrees is 0 degrees.

Therefore, the correct answer is: Set of angle sizes that are multiples of 45 degrees and less than 27 degrees: {0}.