Question

which sentence about measuring angles is true?
an angle that turns through $\frac{10}{360}$ of a circle has a measure of $36^\circ$.
an angle that turns through $\frac{10}{360}$ of a circle has a measure of $10^\circ$.
an angle that turns through $\frac{1}{12}$ of a circle has a measure of $12^\circ$.
an angle that turns through $\frac{1}{12}$ of a circle has a measure of $1^\circ$.

Explanation:

Step1: Calculate full circle angle

A full circle is $360^\circ$.

Step2: Test first option

Multiply fraction by $360^\circ$:
$\frac{10}{360} \times 360^\circ = 10^\circ$? No, wait, correction: $\frac{10}{360} \times 360^\circ = 10^\circ$? Wait no, first option claims $36^\circ$, so it's wrong.

Step3: Test second option

Calculate $\frac{10}{360} \times 360^\circ = 10^\circ$, which matches the option's claim.

Step4: Verify other options

For $\frac{1}{12} \times 360^\circ = 30^\circ$, so third and fourth options are wrong.

Answer:

B. An angle that turns through $\frac{10}{360}$ of a circle has a measure of $10^\circ$.