The statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
Angle
When two straight lines or rays intersect at a shared terminal, an angle is generated. The angle can be measured in degrees or radians.
How to find a true statement about measuring the angle from the given statements?
Let us discuss all four options.
The measure of a whole circle is [tex]360^{o}[/tex]
(A) Here, [tex]\frac{10}{360}\times360=10^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]36^{o}[/tex]" is false.
(B) Here, [tex]\frac{1}{12}\times360=30^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{1}{12}[/tex] of a circle has a measure of [tex]1^{o}[/tex]" is false.
(C) Here, [tex]\frac{10}{360}\times360=10^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
(D) Here, [tex]\frac{1}{12}\times360=30^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{1}{12}[/tex] of a circle has a measure of [tex]12^{o}[/tex]" is false.
Therefore, option (C) is correct.
Hence, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
Learn more about angle here-
https://brainly.com/question/13954458
#SPJ2
