Download 1-5 Angle Relations

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
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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.