1-5 Angle Relations

Special Angle Pairs

Pairs of Angles Some pairs of angles are special because of how they are positioned in relationship to each other. Three of these angle pairs are described below.

Adjacent angles ADJACENT ANGLES are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points EXAMPLE

Linear Pair A LINEAR PAIR is a pair of adjacent angles with non-common sides that are opposite rays.

Vertical Angles VERTICAL ANGLES are two non adjacent angles formed by two intersecting lines.

Angle Pair Relationships

Complementary Angles Complementary Angles are two angles with measures that have a sum of 90 degrees

Supplementary Angles Supplementary angles are two angles that have a sum of 180 degrees.

The angles in a linear pair are supplementary

Acute Angles An angle of fewer than 90 degrees

Obtuse angles An angle greater than 90 degrees

Perpendicular lines Lines, segments, or rays that form right angles are PERPENDICULAR Perpendicular lines intersect to form four right angles Perpendicular lines intersect to form congruent adjacent angles Segments and rays can be perpendicular to lines or other line segments and rays

Perpendicular Lines

Exercise What is another name for l? Name the intersection of l and m? Name three collinear points.

Algebra Angle E and Angle F are supplementary. The measure of Angle E is 54 more than the measure of Angle F. Find the measures of each angle.

Algebra The measure of an angle’s supplement is 76 less than the measure of the angle. Find the measure of the angle and its supplement.

Algebra The measure of the supplement of an angle is 40 more than two times the measure of the complement of the angle.

Algebra Angle 3 and Angle 4 form a linear pair. The measure of Angle 3 is four more than three times the measure of Angle 4. Find the measure of each angle.