91Ó°ÊÓ

When you want to draw an angle, it's important to start in **standard position**. In this position, the angle sits on something we call the coordinate plane. What's special about standard position is that the angle's starting point, known as the initial side, is directly on the positive x-axis. Imagine the vertex, or corner point, of the angle right at the origin (0,0) of the coordinate plane. From there, the terminal side of the angle will extend out up or down depending on the degree measure the angle represents. - For example, a 150-degree angle moves counterclockwise since positive angles always go that way. - The initial side will lie flat along the positive x-axis and the terminal side sweeps out to show the measure of the angle.

The **coordinate plane** is like a grid that helps us precisely place and understand angles and points in geometry. In this grid: - There's an x-axis running horizontally. - A y-axis runs vertically up and down. The center of the coordinate plane, where both axes cross each other, is called the origin. It holds the point (0,0). Using this grid helps clearly see where angles are, like when they're in standard position. For example, with a 150-degree angle in standard position, you start on the positive x-axis and move upwards, turning through the coordinate plane. You'll end up placing it in one of the plane's four sections or quadrants.

The **second quadrant** is a specific area on the coordinate plane. It's located to the left of the y-axis and above the x-axis. The plane is divided into four quadrants, and the second quadrant is the place where you'll find angles that: - Are more than 90 degrees but less than 180 degrees. When you draw a 150-degree angle in standard position, you'll go counterclockwise from the positive x-axis, which lands the terminal side in this second quadrant. Knowing which quadrant an angle is in helps you find the reference angle, which is the smallest angle an angle makes with the x-axis. In the second quadrant, the reference angle is determined by subtracting the angle's measure from 180 degrees. That's why the reference angle for our 150-degree angle ends up being 30 degrees.