Question

Order the following angles from the angle with the smallest amount of openness to the angle with the largest amount of openness. Express your answer without any commas. (e.g., ABCD would indicate Angle A has the smallest measure, Angle B has the second smallest measure, etc.)Angle A: An angle that cuts off 13% of the circumference of the circle.Angle B: An angle with a measure of 13 degrees.Angle C: An angle with a measure of 0.13 radians.Angle D: An angle that cuts off 1/13 th of the circumference of the circle.

Answer 1

To order the following angles from the angle with the smallest amount of openness to the angle with the largest amount of openness, let's arrange the angles from the smallest to the largest.

Let's find the exact measure of each angle in degrees.

• Angle A: An angle that cuts off 13% of the circumference of the circle:

Given that the circumference of a circle is 360, we have:

`(13)/(100)\ast360=46.8\text{ degre}es`

Therefore, the angle that cuts off 13% from the circumference is 46.8 degrees

• Angle ,B: An angle with a measure of 13 degrees:

THis measure is already in degrees. The measure of this angle is 13 degrees.

• Angle C: An angle with a measure of 0.13 radians:

To convert rad to degrees, apply the formula below

`0.13\ast(180)/(\pi)=7.4\text{ degr}ees`

The measure of this angle 7.4 degrees

• Angle D: An angle that cuts off 1/13 th of the circumference of the circle:

Given the circumference of a circle is 360 degrees, we have:

`(1)/(13)\ast360=27.7\text{ degre}es`

The measure of this angle is 27.7 degrees.

Arranging this with the angle that has the smallest amount of openness to the largest, we have:

Angle C = 7.4 degrees

Angle B = 13 degrees

Angle D = 27.7 degrees

ANgle A = 46.8 degrees

ANSWER:

Angle C

Angle B

Angle D

Angle A