1. Measuring Angles

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 $m\angle 2=m\angle 3$.

Suppose an angle $\theta$ in standard position has a measure of $140°$. In which quadrant does its terminal side lie?

If an angle $\mathrm{AFE}$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $\mathrm{AFE}$ in degrees?

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

If two angles are in standard position and their terminal sides coincide, and angle 1 has a measure of $50°$, which of the following could be the measure of angle 2?

Given a circle with center $H$ and an arc $EF$ in standard position, what is the measure of arc $EF$ if the central angle is $114°$?

Solve each problem. See Example 6. Surveying One student in a surveying class measures an angle as 74.25°, while another student measures the same angle as 74° 20' . Find the difference between these measurements, both to the nearest minute and to the nearest hundredth of a degree.

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

Which of the following angles in standard position corresponds to a point on the negative $y$-axis?

If $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$ are two angles in standard position, which angle has a measure equal to the sum of $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$?

Given a right triangle where angle $ACB$ is one of the non-right angles and the side opposite angle $ACB$ is $4$ units while the side adjacent to angle $ACB$ is $3$ units, which is the approximate measure of angle $ACB$?

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

If an angle $\mathrm{lkj}$ in standard position has a terminal side that passes through the point $(7,6)$ on the coordinate plane, what is the measure of angle $\mathrm{lkj}$ in degrees, rounded to the nearest whole degree?

In standard position, if $\theta$ = $53°$, what is the reference angle?

Given that angle $psq$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $psq$ in degrees?