4.1 NotesFill in your notes

Adjacent angles share a ______________ and _______, but have no _______________________.vertex side

Points in common

Complementary Angles – Two angles whose measures have a sum of _______. Complementary angles can be ___________ or _____________. If mA = 50 and mB = 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 mA = 85, find mB.  If C and D are supplementary and mC = 85, find mD.

90°adjacent

nonadjacent

complement

180°adjace

ntnonadjacent

supplement

mA + mB = 90° so 85 + mB = 90°mB = 5°

mC + mD = 180° so 85 + mD = 180°mD = 95°

s

s

s

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)

Example: and are complementary angles. Find the measure of the angles if and

LMN PQR

mLMN 4x 2 mPQR9x1

mLMN + mPQR = 90° (definition of complementary angles) 4x -2 + 9x +1 = 90° 13x -1 = 90° 13x = 91° x = 7

mLMN = 4x -2 = 4(7) -2 = 28 – 2 = 26° mPQR = 9x + 1 = 9(7) + 1 = 63 + 1 = 64°

Check: 64 + 26 = 90

432

1

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

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?

432

1

a) b) c)

d) e) f)

truefalse false

false true true

m1 + m2 + m3 + 78 = 180° (makes a straight line)m1 + 90 + 78 = 180° (since 2 and 3 are complementary, they add to 90)m1 + 168 = 180°m1 = 12° m1 = m3 = m4 = 12° m2 + m3 = 90° (since they are complementary)SO… m2 + 12 = 90° and m2 = 78°

yes

no

no

yes

2 and 3

2 and (5 + 4) are vertical angles

5 + 4 = 90 + 60 = 150 SO…. m 2 = 150°

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°

105°

75°

75°

coplanar

collinear

between

B

We don’t know

We don’t know

We don’t know