1. 4.1 Notes Fill in your notes

2. Adjacent angles share a ______________ and _______, but have no _______________________. vertexsidePoints in common

3. Complementary Angles – Two angles whose measures have a sum of _______. Complementary angles can be ___________ or _____________. If m  A = 50  and m  B = 40 , then  A and  B are complementary.  A is the ____________ of  B. Supplementary Angles – Two angles whose measures have a sum of ______. Supplementary angles can be _____________ or _________________.  C and  D are supplementary.  D is the ______________ of  C. If  A and  B are complementary and m  A = 85 , find m  B. If  C and  D are supplementary and m  C = 85 , find m  D. 90° adjacentnonadjacent complement 180° adjacent nonadjacent supplement m  A + m  B = 90° so 85 + m  B = 90° m  B = 5° m  C + m  D = 180° so 85 + m  D = 180° m  D = 95°

4. Name a pair of….. Complementary Supplementary Adjacent  FGK and  GKL (add to 90°)  HGK and  GKL (add to 180°)  FGK and  HGK (share a side and vertex but no common interior points)

5. Example: and are complementary angles. Find the measure of the angles if and m  LMN + m  PQR = 90° (definition of complementary angles) 4x -2 + 9x +1 = 90° 13x -1 = 90° 13x = 91° x = 7 m  LMN = 4x -2 = 4(7) -2 = 28 – 2 = 26° m  PQR = 9x + 1 = 9(7) + 1 = 63 + 1 = 64° Check: 64 + 26 = 90

6. Linear Pair of angles – Two adjacent angles whose _________________sides form ______________. Vertical Angles – Two angles whose sides form ________________________ OR a pair of ______________ angles formed by ________________________________. nonadjacent Noncommon sides Two intersecting lines Opposite rays 2 pairs of opposite rays

7. Vertical Angle Congruence Theorem – Vertical angles are congruent. Example –  1 and  3 are a linear pair.  1 and  4 are a linear pair.  1 and  2 are vertical angles. True or false? a) b)c) d)e)f) truefalse true

8. m  1 + m  2 + m  3 + 78 = 180° (makes a straight line) m  1 + 90 + 78 = 180° (since  2 and  3 are complementary, they add to 90) m  1 + 168 = 180° m  1 = 12° m  1 = m  3 = m  4 = 12° m  2 + m  3 = 90° (since they are complementary) SO… m  2 + 12 = 90° and m  2 = 78°

9. yes no yes  2 and  3  2 and (  5 +  4) are vertical angles  5 +  4 = 90 + 60 = 150 SO…. m  2 = 150°

10.  1 = x and  2 = 3x  1 +  2 = 180° (definition of linear pair) x + 3x = 180° (definition of linear pair) 4x = 180° x = 45°  1 = x and  2 = 3x  1 = 45° and  2 = 135° (4x+15) + (5x + 30) = 180° (makes a straight line) X = 15 (3y + 15) + (3y - 15) = 180° (makes a straight line) y = 30 105° 75°

11. coplanar collinear between B We don’t know