1 5 Angle Pair Relationships Adjacent angles Two

1. 5 : Angle Pair Relationships

Adjacent angles: Two angles that share a common side and vertex 2 1 1 is adjacent to 2

Complementary Angles: Two angles that add to 90° 1 2 m 1 + m 2 = 90°

Supplementary Angles: Two angles that add to 180° 1 2 1 m 1 + m 2 = 180° 2

Linear Pair: Two adjacent angles whose noncommon sides are opposite rays (they form a line) 1 2 They will always add to 180° m 1 + m 2 = 180°

Vertical Angles: Two angles whose sides form two pairs of opposite rays 1 2 They will always be congruent!

1. Tell whether the indicated angles are adjacent. EFG and HGF no

1. Tell whether the indicated angles are adjacent. JNM and MNK yes

2. Name a pair of complementary angles, supplementary angles, and vertical angles. Vertical: ROL and NOP L M R N O Q P LOM and QOP Complementary: QOR and ROL MON and NOP Supplementary: ROL and LON ROM and MON QOL and LOM

2. Name a pair of complementary angles, supplementary angles, and vertical angles. Vertical: DGE and BGC A E EGB and DGC B D G C Complementary: DGE and EGA Supplementary: DGE and EGB DGA and AGB EGA and AGC

3. 1 and 2 are complementary angles. Given the measure of 1, find m 2. m 1 = 82° m 2 = 90 – 82 = 8°

3. 1 and 2 are complementary angles. Given the measure of 1, find m 2. m 1 = 23° m 2 = 90 – 23 = 67°

4. 1 and 2 are supplementary angles. Given the measure of 1, find m 2. m 1 = 82° m 2 = 180 – 82 = 98°

4. 1 and 2 are supplementary angles. Given the measure of 1, find m 2. m 1 = 105° m 2 = 180 – 105 = 75°

5. Find the measure of ABD and DBC. 4 x + 6 + 11 x – 6 = 180 15 x = 180 x = 12 m ABD = 4(12)+6 = 48+6 = 54° m DBC = 11(12)-6 = 132 -6 = 126°

5. Find the measure of ABD and DBC. 2 x + 3 x = 90 5 x = 90 x = 18 m ABD = 2(18) = 36° m DBC = 3(18) = 54°

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 2 Linear pair

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 3 Vertical angles

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 2 and 4 Vertical angles

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 7 neither

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 8 neither

7. Find the values of x and y. 6 x – 11 + 2 x – 9 = 180 8 x – 20 = 180 8 x = 200 x = 25° 20 y + 19 + 2 x – 9 = 180 20 y + 19 + 2(25) – 9 = 180 20 y + 60 = 180 20 y = 120 y = 6°

7. Find the values of x and y. 21 x – 3 + 5 x + 1 = 180 26 x – 2 = 180 26 x = 182 x = 7° 4 y + 17 y – 9 = 180 21 y = 189 y = 9°