Unit 1 Describe Angle Pair Relationships Adjacent angles

Unit 1 Describe 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 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 NOP L M R N O Q P LOM QOP Complementary: m QOR + m ROL = 90 m MON + m NOP = 90 Supplementary: m ROL + m LON = 180 m ROM + m MON = 180 m QOL + m LOM = 180

2. Name a pair of complementary angles, supplementary angles, and vertical angles. Vertical: DGE BGC A EGB DGC E D Complementary: B m DGE + m EGA = 90 G C Supplementary: m DGE + m EGB = 180 m DGA + m AGB = 180 m EGA + m AGC = 180

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°