Find the supplement of the radian measure 7 π /8. Express your answer in terms of π .
Remember a while back when you had, say, 36 degrees; and you had to find the supplement ?
You set up this equation: $\displaystyle 36 + x = 180$
And then solved for $\displaystyle x$.
We do the same, except now it's gonna be in terms of $\displaystyle \pi$.
So: $\displaystyle \frac{7\pi}{8} + x = 180 $
$\displaystyle x = 180 - \frac{7\pi}{8}$
Subbing $\displaystyle 2\pi$ for $\displaystyle 180$ will make this easier:
$\displaystyle x = 2\pi - \frac{7\pi}{8}$
Get that common denominator: $\displaystyle \frac{16\pi}{8} - \frac{7\pi}{8} = \frac{16\pi - 7\pi}{8} = \boxed{\frac{9\pi}{8}}\;\;radians$