To convert the measure of angle [tex]\( T \)[/tex] from radians to degrees, we use the conversion factor that [tex]\( 180 \)[/tex] degrees is equal to [tex]\( \pi \)[/tex] radians.
Given that the measure of angle [tex]\( T \)[/tex] is [tex]\( \frac{49 \pi}{60} \)[/tex] radians, we need to determine its equivalent in degrees. Here are the steps to find the solution:
1. Write down the formula for converting radians to degrees:
[tex]\[
\text{Degrees} = \text{Radians} \times \frac{180}{\pi}
\][/tex]
2. Substitute the given angle [tex]\( T \)[/tex] into the formula:
[tex]\[
\text{Degrees} = \left( \frac{49 \pi}{60} \right) \times \frac{180}{\pi}
\][/tex]
3. Simplify the equation by canceling out [tex]\( \pi \)[/tex] from the numerator and the denominator:
[tex]\[
\text{Degrees} = \frac{49 \times 180}{60}
\][/tex]
4. Calculate the multiplication and division:
[tex]\[
\text{Degrees} = \frac{8820}{60}
\][/tex]
5. Perform the division:
[tex]\[
\text{Degrees} = 147
\][/tex]
Therefore, the measure of angle [tex]\( T \)[/tex] in degrees is:
[tex]\[
\boxed{147}
\][/tex]
