Answer
a. $ 0.3\pi$
b. $\approx 0.84$
c. $0$
Work Step by Step
The reference angle $\overline{\theta}$ associated with an angle $\theta$
is the acute angle formed by the terminal side of $\theta$ and the x-axis.
a.
$\theta=2.3\pi=2\pi+0.3\pi$
has terminal side in quadrant I.
The acute angle it forms with the x-axis is
$\overline{\theta}=0.3\pi.$
b.
$\theta=$2.3 has terminal side in quadrant II.
($\displaystyle \frac{\pi}{2} < 2.3 < \pi)$
The acute angle it forms with the x-axis is
$\overline{\theta}=\pi-2.3\approx 0.84$
c.
$-10\pi=-5(2\pi)$, so its termminal side is
the positive x-axis.
The reference angle is $\overline{\theta}=0$
