Determine the correct formula for the measures of all angles coterminal with the angle: 140°
a. 140° + (360° + n)
b. 140° + n(360°)
c. 360° + n(180°)
d. 360° + (180° + n)
thankyou (:
To determine the correct formula for the measures of all angles coterminal with an angle, you need to understand what it means for angles to be coterminal.
Coterminal angles are angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees. In other words, if you take an angle and add or subtract 360 degrees (or any multiple of 360 degrees), you will get a coterminal angle.
So, let's analyze the given options:
a. 140° + (360° + n): This option suggests that you add 360° and n to the angle. However, n could be any number, and you don't need to add 360° and n together. This formula is not correct.
b. 140° + n(360°): This option suggests that you multiply n by 360° and add it to the angle. This is the correct formula for finding coterminal angles. By choosing different values for n, you can generate all angles that are coterminal with 140°.
c. 360° + n(180°): This option suggests that you multiply n by 180° and add it to 360°. While this formula can generate angles, it does not produce angles that are coterminal with 140° specifically. This formula is not correct.
d. 360° + (180° + n): This option suggests that you add 180° and n together, and then add 360° to the result. Similar to option c, this formula does not specifically generate angles that are coterminal with 140°. This formula is not correct.
Therefore, the correct formula for the measures of all angles coterminal with 140° is:
b. 140° + n(360°)
360° is one complete rotation, so any multiple of that ends up in the same place.
So, (b)