Given that angle 2 has measure $m\angle 2=a+15°$ and angle 3 has measure $m\angle 3=a+35°$, find the value of $a$ such that $m\angle 2=m\angle 3$.

In standard position, if ray $OX$ is the initial side and ray $OZ$ is the terminal side, what is the name of the angle formed by these two rays?

An angle in standard position has its terminal side passing through the point $(0,-1)$ on the unit circle. Estimate the measure of this angle to the nearest one-half radian.

If an angle is formed by a $270°$ clockwise rotation from the positive x-axis, what is its measure in standard position?

An angle in standard position has its terminal side passing through the point $\left(3,,,4\right)$ in the coordinate plane. Estimate the measure of this angle within $10°$.

Point E is located at coordinates $(0,1)$ on the terminal side of an angle in standard position. What is the measure of this angle in degrees?

If ray $\overrightarrow{\mathrm{AB}}$ is rotated counterclockwise about the origin to coincide with ray $\overrightarrow{\mathrm{AC}}$ in standard position, and the measure of angle $\angle BAC$ is $120$ degrees, how many degrees has $\mathrm{ABC}$ been rotated counterclockwise about the origin?

If an angle in standard position has its terminal side passing through the point $(0,1)$ on the unit circle, what is the measure of the angle in degrees?

If $\theta$ is in standard position and its terminal side passes through the point $(2,3)$, what is the degree measure of $\theta$ rounded to the nearest whole number?