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1.5 –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 1 2 m1 + m2 = 90° Supplementary Angles: Two angles that add to 180° 1 2 1 m1 + m2 = 180° 2 Linear Pair: Two adjacent angles whose noncommon sides are opposite rays 1 2 They will always add to 180° m1 + m2 = 180° Vertical Angles: Two angles whose sides form two pairs of opposite rays 1 2 They will always be congruent! 1 2 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 . Complementary: QOR and ROL MON and NOP L M R N O Q Supplementary: ROL and LON ROM and MON QOL and LOM P Vertical: ROL and NOP LOM and QOP 2. Name a pair of complementary angles, supplementary angles, and vertical angles . Complementary: DGE and EGA A E D G B C Supplementary: DGE and EGB DGA and AGB EGA and AGC Vertical: DGE and BGC EGB and DGC 3. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 90 – 82 = 8° 3. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 23° m2 = 90 – 23 = 67° 4. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 180 – 82 = 98° 4. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 105° m2 = 180 – 105 = 75° 5. Find the measure of ABD and DBC. 4x + 6 + 11x – 6 = 180 15x = 180 x = 12 mABD = 4(12)+6 = 48+6 = 54° mDBC = 11(12)-6 = 132-6 = 126° 5. Find the measure of ABD and DBC. 2x + 3x = 90 5x = 90 x = 18 mABD = 2(18) = 36° mDBC = 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. 16x + 9x + 5 = 180 25x + 5 = 180 25x = 175 x = 7° 16x + 4y = 180 16(7) + 4y = 180 112 + 4y = 180 4y = 68 y = 17° 7. Find the values of x and y. 6x – 11 + 2x – 9 = 180 8x – 20 = 180 8x = 200 x = 25° 20y + 19 + 2x – 9 = 180 20y + 19 + 2(25) – 9 = 180 20y + 60 = 180 20y = 120 y = 6° 7. Find the values of x and y. 9x + 2 + 10x + 7 = 180 19x + 9 = 180 19x = 171 x = 9° 18y + 25 + 9x + 2 = 180 18y + 25 + 9(9) + 2 = 180 18y + 108 = 180 18y = 72 y = 4°