1. Measuring Angles

If an angle in standard position has its terminal side passing through the point $(-3,4)$, what is the measure of the angle in degrees?

If angle $\mathrm{gfd}$ is in standard position and its terminal side lies along the positive $y$-axis, what is its measure?

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

Given that $m\angle klh$ = $120°$ and $m\angle klm$ = $180°$, what is the measure of the angle between the terminal sides of these two angles in standard position?

If an angle in standard position has its terminal side passing through the point $B(-3,4)$ in the coordinate plane, what is the measure of angle $BCD$ to the nearest degree?

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?

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 174.255°

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.

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

1/ sec 14.8°

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

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