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Reference Angle

In the field of geometry and mathematics, there are many different types of angles. Understanding the various properties of these angles can help us solve a range of different problems. So what exactly is a "reference angle?" Let''s find out:

Reference angles, explained

A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.

To understand this definition, we need to understand the meaning of "terminal side."

The terminal side of an angle is the side that defines the angle. When we see most angles, they are displayed with a horizontal x-axis. This x-axis includes an "origin" which is usually (0,0). This origin forms the vertex of the given angle. The terminal side can be anywhere, while the x-axis is fixed. This is why we say that the terminal side "defines" the angle.

Therefore, a reference angle is the smallest of the two angles possible in a linear pair. If we know that we are measuring from the x-axis, then the reference angle must be 90 degrees or less. For example, a reference angle of 35 degrees would mean that the rest of the angle must equal 145 degrees.

Visualizing the reference angle

It helps to visualize how the reference angle works:

In this example, we can see that the reference angle exists in quadrant I.

In this example, we see that the reference angle lies on quadrant II. This means that its degrees are negative.

In this example, we see that the reference angle lies on quadrant III. This means that we subtract 180 degrees from the non-reference angle.

In this example, we see that the reference angle lies on quadrant IV. This means we must subtract the non-reference angle from 360 degrees.

Topics related to the Reference Angle

Coterminal Angles

Angles of Elevation and Depression

Complementary Angles

Flashcards covering the Reference Angle

Basic Geometry Flashcards

Common Core: High School - Geometry Flashcards

Practice tests covering the Reference Angle

Common Core: High School - Geometry Diagnostic Tests

Basic Geometry Diagnostic Tests

Hotmath can help with reference angles

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