Properties of Angles

Before working through the information below you may wish to review this lesson on measuring angles as well as taking a look at the lesson on adding and subtracting angles.

This lesson will provide information and guidance on:

After reviewing the lessons above you will be ready to read through the information below on angles and their relationships with your children. Discuss these as you go and, when you are ready, try the angle relationships worksheet.

Useful Terms

Parallel Lines - lines that are equidistant from each other and never intersect.

Transversal - a line that intersects two or more other lines.

Adjacent Angles - angles that share a common side and that have a common vertex.

Complementary Angles

Complementary Angles are those which add together to make 90°.

two adjacent angles with common vertex forming right angle ∠ABD + ∠DBC = 90°

a 60 and a 30 degree angle that are adjacent and that share a common vertex

These two angles are complementary because they add together to make 90°.

60° + 30° = 90°

a 15 abd a 75 degree angle that are not adjacent nor share a vertex

These two angles are also complementary.

15° + 75 ° = 90°

The examples above all show two angles that are complementary. Notice that the angles do not have to be adjacent to be complementary. If they are adjacent then they form a right angle.

Supplementary Angles

Supplementary Angles add together to make 180°

a 125 and a 55 degree angle that are adjacent and that together form a 180 degree angle

125° + 55° = 180°

The two angles shown above are supplementary to each other. They add together to give 180°. They can be said supplement each other. Note that, as with complementary angles, they do not need to be adjacent to each other.

Opposite Angles

When to lines intersect they create four angles. Each angle is opposite to another and form a pair of what are called opposite angles.

intesecting lines with opposite angles shown - a & c and b & d intersecting lines with 130 and 50 degree angles shown

Angles a and c are opposite angles.

Angles b and d are opposite angles

Opposite angles are equal. The two 130° angles are opposite as are the two 50° angles.

Opposite angles are sometimes called vertical angles or vertically opposite angles.

Corresponding and Alternate Angles

The example below shows two parallel lines and a transversal (a line that cross two or more other lines). This results in eight angles. Each of these angles has a corresponding angle. Looking at the two intersections, the angles that are in the same relative (or corresponding) positions are called corresponding angles.

Since the two lines are parallel, the corresponding angles are equal.

2 parallel lines with transversal and 8 angles annotated

a and e are corresponding angles

b and f are corresponding angles

c and g are corresponding angles

d and h are corresponding angles

As Shown below, there are also two pairs of alternate interior angles and two pairs of alternate exterior angles. Notice how the interior angles are in between the two parallel lines and the exterior angles are to the outside.

2 parallel lines and a transversal with eight alternate angles shown

a and g are alternate exterior angles

b and h are alternate exterior angles

c and e are alternate interior angles

d and f are alternate interior angles

Since the two lines are parallel, the alternate angles shown above are equal.

The Sum of Interior Angles

illustration of how the three interior angles of a triangle can be arranged to show a total angle of 180 degrees

The sum of the interior angles in a triangle is 180°.

illustration of how the four interior angles of a quadrilateral can be arranged to show a total angle of 360 degrees

The sum of the interior angles in a quadrilateral is 360°.

Try the 180° In a Triangle Experiment which is a 2-page (be careful with the scissors) activity to demonstrate that the sum of the interior angles in a triangle is 180°.

Angle Relationship Worksheet

Have your children try the worksheet below that has questions on angle relationships. After completing it your children will be ready to review the lesson on finding missing angles.

All Geometry 24 Worksheets Terms/ Definitions Formulas/ Equations 2D Shapes Defining Attributes 3D Shapes Quadrilaterals Measuring Angles Using a Protractor Adding and Subtracting Angles Angle Properties Finding Angles Symmetry Area Volume Surface Area Perimeter Coordinate System Coordinate Graphing Pythagoras' Theorem Distance Between Two Points Congruent Triangles Similar Triangles Transformations Dilations