Angle Relationships

Definitions Adjacent Angles – two angles that lie in the same plane, have a common vertex, and a common side but no common interior points 1  1 is adjacent to  2 C 2 Non example 3 4

Definitions Vertical Angles – two non-adjacent angles formed by intersecting lines. Non Example J FKG is vertical to JKH F 7 8 K H G  FKJ is vertical to  GKH

Definitions Linear Pair – a pair of adjacent angles whose non-common sides are opposite rays. Y T W R  RTW and  WTY are a linear pair

Angle Relationships Complementary Angles – two angles whose measures have a sum of 90 L m RXQ + m LFM = 27+ 63 = 90 X 63 R 27 M F Q 1 2 m 1 + m 2 = 90

Angle Relationships Supplementary Angles – two angles whose measures have a sum of 180. D H 77 5 P C B 4 103 m 4 + m5 = 180 T m DCB + m HPT = 77 + 103 = 180

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 to other line segments and rays. The right angle symbol in the figure indicates that the lines are perpendicular.  is read “is perpendicular to”

Perpendicular R A B AB  RT T

Work this problem M Find x so that KO  HM N K O (3x + 6) I 9x 3x + 6 + 9x = 90 12 x + 6 = 90 H -6 -6 12x = 84 12 12 x = 7