1. Measuring Angles

Given a circle with center O and points A, B, and C on the circumference such that angle $\angle AOB$ is $72°$ and angle $\angle BOC$ is also $72°$, what is the measure of angle $\angle CBE$ if E is the point where the extension of $OB$ meets the circle again?

Which of the following is defined using the undefined terms $\mathrm{point}$ and $\mathrm{line}$?

An angle formed by the intersection of two adjacent sides of a polygon is called a(n) $?$ angle.

Given the following angle measures in standard position: $95°$, $105°$, $119°$, and $180°$, which angle has the greatest measure?

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 275.1005°

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

If angle $\mathrm{COA}$ is in standard position and its terminal side passes through the point (−$1$, $2$), what is the measure of angle $\mathrm{COA}$ to the nearest degree?

Give two positive and two negative angles that are coterminal with the given quadrantal angle. 270°

Line $ef$ is tangent to circle $g$ at point $a$. If the measure of angle $eag$ is $95°$, what is the measure of the angle between the tangent and the radius at point $a$?

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/csc(90°-51°)

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I: 1.

tan 16°

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858

F. 1.962610506

G. 14.47751219°

H. 1.015426612

I. 1.051462224

J. 0.9925461516

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 an angle in standard position has its terminal side passing through the point $(2,5)$ in the coordinate plane, what is the measure of the angle (in degrees) to the nearest tenth? $42.5°$ $67.5°$ $85°$ $135°$

In Exercises 8–12, draw each angle in standard position. 8𝜋 3

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 174 °