Question

Which sentence about measuring angles is true?

A. An angle that turns through 2 of a circle has a measure of 1°.
B. An angle that turns through 360 of a circle has a measure of 36º.
C. An angle that turns through 1/10 of a circle has a measure of 12°.
D. An angle that turns through 10/360 of a circle has a measure of 10°.

Answer 1

The true statement about measuring angles is D. An angle that turns through 10/360 of a circle has a measure of 10°, as one complete revolution of a circle equals 360°.

Step-by-step explanation:

The question you have asked is about measuring angles in a circle. One complete revolution of a circle is equal to 360 degrees. Therefore, to determine the degree measure of an angle based on its proportion of the circle, we multiply the fraction of the circle by 360 degrees.

• An angle that turns through 1/360 of a circle has a measure of 1°.
• An angle that turns through 360/360 or one whole circle has a measure of 360°.
• An angle that turns through 1/10 of a circle has a measure of 1/10 * 360°, which is 36°.
• An angle that turns through 10/360 of a circle has a measure of 10/360 * 360°, which simplifies to 10°.

Based on this information, the correct statement is D. An angle that turns through 10/360 of a circle has a measure of 10°.