Do NOW If mABD = (6x + 4)° and mDBC = (8x – 4), and 𝑺𝑷 bisects, justify using a proof. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Page 24 18) 25° 19) Acute 20) Right 21) 22) Obtuse 32) 72° 41) D 42) H 29) Statements Reasons 1) mAOC = 7x – 2, mDOC = 2x + 8 and mEOD = 27 1) Given 2) mAOC + mCOD + mDOE = mAOE 2) Given 3) (7x – 2) + (2x + 8) + 27 = 180° 3) Substitution 4) 9x + 33 = 180 – 33 – 33 4) Combine Like Terms 5) 𝟗𝒙 𝟗 = 𝟏𝟒𝟕 𝟑𝟑 6) Substitution P.O.E. 7) x = 49/11 or 16 1/3 7) Division P.O.E. 18) 25° 19) Acute 20) Right 21) 22) Obtuse 32) 72° 41) D 42) H 43) C 44) J 17) Statements Reasons 1) mRSP = 3x – 2, mPST = 9x – 26, and 𝑺𝑷 bisects Given 2) mRSP = mPST 2) Def’n Angle Bisector 3) (3x – 2)° = (9x – 26)° –9x –9x 3) Substitution 4) –6x – 2 = –26 + 2 + 2 4) Subtraction P.O.E. 5) −𝟔𝒙 −𝟔 = −𝟐𝟒 −𝟔 5) Addition P.O.E. 6) x = 4 6) Division P.O.E. 7) mRST = mRSP + mPST 7) Angle Addition Post. 8) mRST = 3x – 2 + 9x – 26 8) Substitution 9) mRST = 12x – 28 = 12(4) – 28 9) Combine Like Terms 10) mRST = 20° 10) Substitution 31) Statements Reasons 1) mAOB = 6x + 5, mBOC = 4x – 2 and mAOC = 8x + 21 1) Given 2) mAOB + mBOC = mAOC 2) Angle Addition Post. 3) 6x + 5 + 4x – 2 = 8x + 21 3) Substitution 4) 10x + 3 = 8x + 21 – 3 – 3 4) Combine Like Terms 5) 10x = 8x + 18 – 8x –8x 5) Subtraction P.O.E. 6) 𝟐𝒙 𝟐 = 𝟏𝟖 𝟐 6) Substitution P.O.E. 7) x = 9 7) Division P.O.E. 2/18/2019 11:34 PM 1–4: Pairs of Angles

2/18/2019 11:34 PM 1–4: Pairs of Angles

Section 1–4 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us Pairs of Angles Section 1–4 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 2/18/2019 11:34 PM 1–4: Pairs of Angles

Definitions Vertical Angles Adjacent angles are two angles in the same plane; Think: NEXT TO Share the common side Have the Same Vertex Have no interior points Are Coplanar Linear Pair of angles is a pair of adjacent angle whose non–common sides are opposite rays; they are supplementary; Think: L Vertical angles are two angles sides form two pairs of opposite rays; Think: VA Angles Vertical 2/18/2019 11:34 PM 1–4: Pairs of Angles

Visual Examples 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 1 Identify all of the vertical angles, adjacent angles, and linear pairs of angles in the figure. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn Identify all of the vertical angles, adjacent angles, and linear pairs of angles in the figure. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 2 Solve for x and y 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 3 Solve for c 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 4 Solve for x and m∠MAT 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn Solve for t and m∠HRN 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 5 Solve for x 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 6 Solve for x 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn Solve for x 2/18/2019 11:34 PM 1–4: Pairs of Angles

Definitions Complementary angles are two angles whose measures have a sum of 90°; Think: Complementary angles make a CORNER Supplementary angles are two angles whose measures have a sum of 180°; Think: Supplementary angles make a STRAIGHT LINE 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 7 What is the complement and supplement angle of 81.2°? 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 8 What is the complement and supplement angle of (7x – 12)°? 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn What is the complement and supplement angle of (6x + 5)°? 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 9 An angle is 50° smaller than its supplement. Find the two angles. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 10 An angle exceeds its complement by 10°. What is the angle? 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn An angle is triple its supplement. What is the angle? 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 11 An angle is 48° less than one-third its supplement. Find the two angles. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Your Turn An angle is 26° less than one-fourth its supplement. Find the two angles. 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 5 Solve for x and m∠GEO and justify with a proof 2/18/2019 11:34 PM 1–4: Pairs of Angles

Example 5 Solve for x and m∠GEO and justify with a proof 2/18/2019 11:34 PM 1–4: Pairs of Angles