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Angle Pairs Adjacent Angles Definition: Two angles that share a common vertex and side but no common interior points. Examples: A B 36° 22° 1 C 2 D 4 3 Adjacent Angles( a common side ) 1 and 2 are adjacent. 1 and ADC are not adjacent. Non-Adjacent Angles 3 and 4 are not adjacent. Complementary Angles Definition: A pair of angles whose sum is 90˚ Examples: m2 = 50° A B 2 Q A B F 2 1 C Adjacent Angles ( a common side ) m1 = 40° Q 1 R G Non-Adjacent Angles Supplementary Angles Definition: A pair of angles whose sum is 180˚ Examples: B Adjacent supplementary angles are also called “Linear Pair.” 2 1 Q A C B F m1 = 40° m2 = 140° Non-Adjacent Angles 2 A 1 Q R G Examples < 1 and < 2 are complementary angles. Given m < 1, find m < 2. a. m1 52 b. m1 19 < 3 and < 4 are supplementary angles. Given m < 3, find m < 4. a. m3 147 b. m4 38 Examples < A and < B are complementary angles. Find m < A & m < B. m A 5x 4 m B 7 x 10 < C and < D are supplementary angles. Find m < C & m < D. m C 7 x 3 m D x 1 Linear Pair Definition:Two adjacent angles are a linear pair if their non-common sides are opposite rays. The angles in a linear pair are supplementary. Vertical Angles Definition: A pair of angles whose sides form opposite rays. Vertical angles are congruent. A 1 1 and 3 4 2 and 4 D B Q 2 3 C Vertical angles are non-adjacent angles formed by intersecting lines. Examples What are the linear pairs? What are the vertical angles? Examples <1&<3 neither <2&<3 neither <4&<5 Linear pair <8&<5 Vertical angles <6&<7 Linear pair <4&<9 Vertical angles < 1 & < 2 & < 3 neither Example: If m4 = 67º, find the measures of all other angles. Step 1: Mark the figure with given info. Step 2: Write an equation. m3 m4 180 m3 67 180 67º 3 4 2 1 m3 180 67 113 Because 4 and 2 arevertical angles, they are equal. m4 m2 67 Because 3 and 1 are vertical angles, they are equal. m3 m1 117 Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles. Answers: m4 23 (1 & 4 are vertical angles.) m5 32 (2 & 5 are vertical angles.) m1 m2 m3 180 2 23 32 m3 180 m3 180 55 125 m3 m6 125 3 & 6 are vertical angles. 1 3 6 4 5 Example: If m 1 = 44º, m 7 = 77º find the measures of all other angles. Answers: m3 90 m1 m4 44 m4 m5 90 44 m5 90 m5 46 m6 m7 90 m6 65 90 m6 25 4 5 6 3 2 1 7

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