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ACT Plane Geometry – Angle Review

Angles are a big part of the ACT Plane Geometry section and you should expect to have several questions related to angles, not including the questions that deal with angles and trigonometry.  An angle review will be helpful for you.

Let’s start by make sure we understand some of the terminology regarding angles.

For the purposes of the ACT test, an angle is formed anytime two lines meet or intersect.   For example the following figures show a number of angles:


The vertex is the point where the lines meet that form the angle.  The vertex in the figure on the left is at point M.

The lines or rays that meet to form the angle are usually called the sides of the angle.

The number of degrees tells the size of the angle.  Think of it as the difference in the direction of the two sides of the angle.

The symbol ‘∠’ is sometimes used to designate an angle.

Angles can be referred to in several ways:

  • By the letter of the vertex.  For example, you may see the angle referred to as ∠ A.
  • By a number of letter or number on the interior of the angle (like those in the second and third figures above). This could also be referred to as ∠ A or ∠ 1.
  • By a set of three letters that represent a point on one side, the vertex, and a point on the other side.  This would look like ∠ LMP.  The center letter is always the vertex (or where the lines meet to form the angle).

There’s one exception to the thought that an angle is made where two lines intersect.  That is where you have a single line.  Technically you could think of the single line as two lines that connect at the vertex, but frequently that vertex is not shown.  The angle formed by a single line is 180°.

That’s probably enough of angles for now.  Next we’ll talk about some specific angles and how they are important on the ACT Test.


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