Answer
$(a)$ We define Standard Position of an angle if it is drawn in $xy$-plane with vertex at the origin and its initial side on the positive $x$-axis.
See the example on the image (Taken from chapter $6.1$) below.
$(b)$ Two angles in Standard Position are considered as Coterminal if their sides coincide. We get Coterminal angles by full rotation of one angle.
See the graphs $(a)$ and $(c)$ on the image below.
$(c)$ Yes, $25°$ and $745°$ are coterminal angles.
$(d)$ Reference angle for an angle $\theta$ is the acute angle formed by the terminal side of $\theta$ and the $x$-axis.
$(e)$ The reference angle is $30°$
Work Step by Step
$(a)$ We define Standard Position of an angle if it is drawn in $xy$-plane with vertex at the origin and its initial side on the positive $x$-axis.
See the example on the image (Taken from chapter $6.1$) below.
$(b)$ Two angles in Standard Position are considered as Coterminal if their sides coincide. We get Coterminal angles by full rotation of one angle.
See the graphs $(a)$ and $(c)$ on the image below.
$(c)$ Yes, $25°$ and $745°$ are coterminal angles.
If we full rotate $25°$ $2$ times, that is $25°+360°+360°=745°$, we will see that they are coterminal angles.
$(d)$ Reference angle for an angle $\theta$ is the acute angle formed by the terminal side of $\theta$ and the $x$-axis.
To find the reference angle, it's very useful to know the quadrant in which the terminal side of the angle $\theta$ lies.
Here are formulas to calculate the reference angle for given quadrants:
$I$
The angle is already acute, so the reference angle is $\theta$ itself.
$II$
$180°-\theta$
$III$
$\theta - 180°$
$IV$
$360°-\theta$
$(e)$
The angle is in second quadrant, so using the formula mentioned in $d$ we can calculate:
$180°-150°=30°$
