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Lesson 9.2 Angle Relationships and Parallel Lines . Types of Angles Acute - Angles that measure less than 90. Right - Angles that measure exactly 90. Obtuse -Angles that measure more than 90 and less than 180. Adjacent Angles • Share a vertex and a side but no points in the interiors. <AXB and <BXC are adjacent angles B A X C <AXC and <BXC are not adjacent angles Why? Complementary Angles - Angles whose sum is 90 . a b ma mb 90 x y mx my 90 Complementary angles do not have to be adjacent. Supplementary Angles - Angles whose sum is 180 . k t mk mt 180 b c mb mc 180 Supplementary angles do not have to be adjacent. Congruent Angles • Angles that have the same measurement • Notation: 1 3 m 1 m 3 Vertical Angles - Opposite angles that are formed by intersecting lines. a Opposite angles (vertical angles) are ALWAYS congruent. b a b Identifying Corresponding Angles Transversal -A line that intersects two other lines. Identifying Corresponding Angles Corresponding - Two angles that are formed by two lines and a transversal and occupy Angles corresponding positions. A C 1 2 3 4 5 6 7 8 B D Corresponding Angles If the two lines are parallel, then the corresponding angles are congruent. 1 5 2 6 3 7 4 8 Identifying Alternate Interior Angles Alternate Interior Angles: -interior of a pair of lines on opposite sides of the transversal. A C 1 2 3 4 5 6 7 8 B D Corresponding Angles If the two lines are parallel, then the alternate interior angles are congruent. 3 6 4 5 Find the value of n. 1) 2) n (4n 30) (n 10) (2n 30) n (2n 30) 90 3n 30 90 30 30 3n 60 3 3 n 20 (4n 30) (n 10) 180 5n 20 180 20 20 5n 160 5 5 n 32 Homework • Page 452 -453 (1-11 all and 13) • Draw figures in the homework