Angles

Angles can be classified by their measures.

Types of Angles:
An acute angle is an angle whose measure is less than 90 $LaTeX: ^\circ$ .
A right angle is an angle whose measure is equal to 90 $LaTeX: ^\circ$ .
An obtuse angle is an angle whose measure is greater than 90 $LaTeX: ^\circ$ but less than 180 $LaTeX: ^\circ$ .
A straight angle is an angle whose measure is equal to 180 $LaTeX: ^\circ$ .

Try to match the angles below.

Prior to today, you may have not thought about the "beginning" and "end" of an angle. But for today's lesson (and future lessons) we need to think about the initial and terminal side of angles. We will consider angles in standard position. An angle is in standard position when the vertex is at the origin and the initial side lies on the positive side of the x-axis.

image of vertex on the x-axis of a graph with a terminal side and an initial side

We also consider the measure of angles to be "positive" or "negative" depending on the direction of the angle of rotation.

If an angle rotates more than 360°, you may end up with co-terminal angles. Coterminal angles share the same initial side and terminal side of an angle of rotation. You can think of the coterminal angles as "landing" in the same location after rotating.

image of angle rotating ore than 360° (with 390° and 30° labelled) and terminal side and initial side

BUT DON'T FORGET...each quadrant in the coordinate plane is numbered:

graph with x-axis and y-axis, and quadrants I, II, III, and IV labelled

Check your understanding by matching the angles below:

If an angle is given to you in radians, you can add or subtract equation image indicator $2π$ to find a coterminal angle.

IMAGES CREATED BY GAVS