5 Angles
Learning Objectives
- Understand How to Draw and Name Angles
- Understand Complimentary and Supplementary Angles
- Describe Vertical and Interior Angles
- Find the Sum of the Measures of the Interior Angles of a Convex Polygon with n Sides
- Describe Angle Bisectors
Angles
An angle is formed by two rays that have the same starting point, the vertex. Angles can be named in several ways:
- Using the vertex and a name (letter) from each arm.
- Using the vertex only.
- Using a number.
The symbol [latex]\angle[/latex] represents an angle, for example an angle named “A” is written as [latex]\angle A[/latex].
Examples
Below are pictures of angle followed by their conventional naming.
Complementary and Supplementary Angles
They may be adjacent to each other or not. The total measure is what makes them complimentary.
They may be adjacent to each other or not. The total measure is what makes them supplementary.
Examples
- Find the supplementary angles in this figure and name them correctly.
Solution: 
2. Which of the following angles are complementary?
Solution: 
Vertical and Interior Angles
Vertical Angles are created when two lines intersect each other. In the figure, angles a and c, b and d, e and g, along with f and h make up the vertical angle pairs.
Interior Anglesare formed one of two ways:
- The angles that lie inside a polygon as shown in these quadrilaterals.
- The angles formed when a line, called a transversal, cuts through two parallel lines. The interior angles are the ones that lie in the area enclosed between the parallel lines. So, because lines AB̅ and CD̅ are given as parallel, the interior angles in this figure are W, X, Y and Z.
Sum of the Measures of the Interior Angles of a Convex Polygon with n Sides
The sum of the measures of the interior angles of an n-sided polygon is given by the formula:
(n-2) x 180o
Thus, you only need to know the number of sides of the polygon to determine the total measure of the interior angles.
Examples
- Find the total interior angle measure of a 5-sided polygon.
Solution:
2. Find the total interior angle measure of a 23-sided polygon.
Solution: 
Angle Bisectors
An angle bisector is a ray that divides an angle into two equal parts. In this figure, ∠AOB is bisected by ray OP.
Examples
Name the angle bisector and the angles formed by the bisection.
Solution: 
Attributions
- Content and structure adapted from RSCC Math 1410/1420 OER Team, 2022, CC BY 4.0.
- Images:
- https://commons.wikimedia.org/wiki/File:Corresponding_angles_3.svg
- https://commons.wikimedia.org/wiki/File:Interior_Angle_(PSF).png
- https://commons.wikimedia.org/wiki/File:Angle_bisector_OP.svg
- https://commons.wikimedia.org/wiki/File:Bisector_theorem2.svg
