Can you help me with 1-5 please EXAMPLE 2 Find measures of a complement and a supplementa. Given that Z1 is a complement of 2 and m21 = 68°, find m2.b. Given that 23 is a supplement of 24 and m24 = 56", find m23.READ DIAGRAMSAngles are sometimesnamed with numbers.An angle measure in adiagram has a degreesymbol. An angle namedoes not.Solutiona. You can draw a diagram with complementaryadjacent angles to illustrate the relationship.m22 = 90° – m/1 = 90° – 68° = 22°68°b. You can draw a diagram with supplementaryadjacent angles to illustrate the relationship.m23 = 180° – m4 = 180° – 56° = 124°56°4\3EXAMPLE 3 Find angle measuresREAD DIAGRAMSIn a diagram, you canSPORTS When viewed from the side,the frame of a ball-return net formsassume that a line thata pair of supplementary angleslooks straight is straight. with the ground. Find MZBCE andIn Example 3, B, C, andD lie on BD. So, ZBCD isa straight angle.MZECD.(x+ 2)D(4x + 8)°CB.SolutionSTEP 1 Use the fact that the sum of the measuresof supplementary angles is 180°.MZBCE + MZECD = 180°Write equation.(4x + 8)° + (x + 2)° = 180°Substitute.5x + 10 = 180Combine like terms.5x = 170Subtract 10 from each side.x = 34Divide each side by 5.STEP 2 Evaluate the original expressions when x = 34.M2BCE = (4x + 8)° = (4 • 34 + 8)° = 144°MZECD = (x + 2)° = (34 + 2)° = 36° The angle measures are 144° and 36°.GUIDED PRACTICE for Examples 2 and 33. Given that 21 is a complement of 22 and m2 = 8°, find m21.4. Given that 23 is a supplement of 24 and m23 = 117", find m24.5. ZLMN and Z PQR are complementary angles. Find the measures of theangles if mZLMN = (4x – 2)° and .ZPQR = (9x + 1)°.36Chapter 1 Essentials of Geometry 1.5 Describe Angle PairRelationshipsBeforeYou used angle postulates to measure and classify angles.NowYou will use special angle relationships to find angle measures.Why?So you can find measures in a building, as in Ex. 53.Key Vocabulary• complementaryangles• supplementaryangles• adjacent angles• linear pair• vertical anglesTwo angles are complementary angles if the sum of their measures is 90°.Each angle is the complement of the other. Two angles are supplementaryangles if the sum of their measures is 180°. Each angle is the supplement ofthe other.Complementary angles and supplementary angles can be adjacent anglesor nonadjacent angles. Adjacent angles are two angles that share a commonvertex and side, but have no common interior points.Complementary anglesSupplementary anglesсоммонCORECC.9-12.G.CO.1 Know precisedefinitions of angle, circle,perpendicular line, parallel line,and line segment, based onthe undefined notions of point,line, distance along a line, anddistance around a circular arc.AdjacentNonadjacentAdjacentNonadjacentEXAMPLE 1Identify complements and supplementsIn the figure, name a pair of complementaryangles, a pair of supplementary angles, anda pair of adjacent angles.AVOID ERRORS****.........................*In Example 1, Z DAC andZDAB share a commonvertex. But they sharecommon interior points,so they are not adjacentI 12232SolutionBecause 32° + 58° = 90°, Z BAC and ZRST are complementary angles.Because 122° + 58° = 180°, Z CAD and ZRST are supplementary angles.angles.Because ZBACand ZCAD share a common vertex and side, they are adjacent.GUIDED PRACTICEfor Example 11. In the figure, name a pair of complementaryangles, a pair of supplementarypair of adjacent angles.Ggles, and a41/131°492. Are ZKGH and ZLKG adjacent angles? AreZFGK and ZFGH adjacent angles? Explain.1.5 Describe Angle Pair Relationships35

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Can you help me with 1-5 please EXAMPLE 2 Find measures of a complement and a supplementa. Given that Z1 is a complement of 2 and m21 = 68°, find m2.b. Given that 23 is a supplement of 24 and m24 = 56&#34;, find m23.READ DIAGRAMSAngles are sometimesnamed with numbers.An angle measure in adiagram has a degreesymbol. An angle namedoes not.Solutiona. You can draw a diagram with complementaryadjacent angles to illustrate the relationship.m22 = 90° – m/1 = 90° – 68° = 22°68°b. You can draw a diagram with supplementaryadjacent angles to illustrate the relationship.m23 = 180° – m4 = 180° – 56° = 124°56°4\3EXAMPLE 3 Find angle measuresREAD DIAGRAMSIn a diagram, you canSPORTS When viewed from the side,the frame of a ball-return net formsassume that a line thata pair of supplementary angleslooks straight is straight. with the ground. Find MZBCE andIn Example 3, B, C, andD lie on BD. So, ZBCD isa straight angle.MZECD.(x+ 2)D(4x + 8)°CB.SolutionSTEP 1 Use the fact that the sum of the measuresof supplementary angles is 180°.MZBCE + MZECD = 180°Write equation.(4x + 8)° + (x + 2)° = 180°Substitute.5x + 10 = 180Combine like terms.5x = 170Subtract 10 from each side.x = 34Divide each side by 5.STEP 2 Evaluate the original expressions when x = 34.M2BCE = (4x + 8)° = (4 • 34 + 8)° = 144°MZECD = (x + 2)° = (34 + 2)° = 36°> The angle measures are 144° and 36°.GUIDED PRACTICE for Examples 2 and 33. Given that 21 is a complement of 22 and m2 = 8°, find m21.4. Given that 23 is a supplement of 24 and m23 = 117&#34;, find m24.5. ZLMN and Z PQR are complementary angles. Find the measures of theangles if mZLMN = (4x – 2)° and .ZPQR = (9x + 1)°.36Chapter 1 Essentials of Geometry 1.5 Describe Angle PairRelationshipsBeforeYou used angle postulates to measure and classify angles.NowYou will use special angle relationships to find angle measures.Why?So you can find measures in a building, as in Ex. 53.Key Vocabulary• complementaryangles• supplementaryangles• adjacent angles• linear pair• vertical anglesTwo angles are complementary angles if the sum of their measures is 90°.Each angle is the complement of the other. Two angles are supplementaryangles if the sum of their measures is 180°. Each angle is the supplement ofthe other.Complementary angles and supplementary angles can be adjacent anglesor nonadjacent angles. Adjacent angles are two angles that share a commonvertex and side, but have no common interior points.Complementary anglesSupplementary anglesсоммонCORECC.9-12.G.CO.1 Know precisedefinitions of angle, circle,perpendicular line, parallel line,and line segment, based onthe undefined notions of point,line, distance along a line, anddistance around a circular arc.AdjacentNonadjacentAdjacentNonadjacentEXAMPLE 1Identify complements and supplementsIn the figure, name a pair of complementaryangles, a pair of supplementary angles, anda pair of adjacent angles.AVOID ERRORS****.........................*In Example 1, Z DAC andZDAB share a commonvertex. But they sharecommon interior points,so they are not adjacentI 12232SolutionBecause 32° + 58° = 90°, Z BAC and ZRST are complementary angles.Because 122° + 58° = 180°, Z CAD and ZRST are supplementary angles.angles.Because ZBACand ZCAD share a common vertex and side, they are adjacent.GUIDED PRACTICEfor Example 11. In the figure, name a pair of complementaryangles, a pair of supplementarypair of adjacent angles.Ggles, and a41/131°492. Are ZKGH and ZLKG adjacent angles? AreZFGK and ZFGH adjacent angles? Explain.1.5 Describe Angle Pair Relationships35

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GUIDED PRACTICE for Example 1 1. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. G H 41 131 49 2. Are ZKGH and ZLKG adjacent angles? Are ZFGK and ZFGH adjacent angles? Explain.